{"id":306,"date":"2026-08-12T07:38:54","date_gmt":"2026-08-12T04:08:54","guid":{"rendered":"https:\/\/sciencio.ir\/?p=306"},"modified":"2026-08-12T07:41:59","modified_gmt":"2026-08-12T04:11:59","slug":"5-%d8%b9%d9%85%d9%84%da%af%d8%b1-%d9%85%d9%82%d8%af%d9%85%d9%87","status":"publish","type":"post","link":"https:\/\/sciencio.ir\/?p=306","title":{"rendered":"5 \u0639\u0645\u0644\u06af\u0631 : \u0645\u0642\u062f\u0645\u0647"},"content":{"rendered":"

\u06cc\u06a9\u06cc \u0627\u0632 \u0645\u0641\u0627\u0647\u06cc\u0645 \u0628\u0646\u06cc\u0627\u062f\u06cc \u062f\u0631 \u0635\u0648\u0631\u062a \u0628\u0646\u062f\u06cc \u0645\u06a9\u0627\u0646\u06cc\u06a9 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645\u06cc\u060c \u0639\u0645\u0644\u06af\u0631 \u0627\u0633\u062a. \u062f\u0631 \u0627\u06cc\u0646 \u0641\u0635\u0644 \u0628\u0627 \u062a\u0639\u0631\u06cc\u0641 \u0639\u0645\u0644\u06af\u0631 \u0648 \u0686\u0646\u062f \u0639\u0645\u0644\u06af\u0631 \u062e\u0627\u0635 \u06a9\u0647 \u062f\u0631 \u0645\u06a9\u0627\u0646\u06cc\u06a9 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645 \u06a9\u0627\u0631\u0628\u0631\u062f \u062f\u0627\u0631\u0646\u062f\u061b \u0622\u0634\u0646\u0627 \u0645\u06cc \u0634\u0648\u06cc\u0645.<\/p>\n

1-5 \u062a\u0639\u0631\u06cc\u0641<\/h3>\n

\u0639\u0645\u0644\u06af\u0631 \u0642\u0627\u0639\u062f\u0647 \u0627\u06cc \u0631\u06cc\u0627\u0636\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0627\u06af\u0631 \u0628\u0631 \u06cc\u06a9 \u0628\u0631\u062f\u0627\u0631\u062d\u0627\u0644\u062a \u06a9\u062a \u0627\u0639\u0645\u0627\u0644 \u0634\u0648\u062f\u060c \u06a9\u062a \u062f\u06cc\u06af\u0631\u06cc \u0646\u062a\u06cc\u062c\u0647 \u0645\u06cc \u062f\u0647\u062f \u0648 \u0627\u06af\u0631 \u0628\u0631 \u06cc\u06a9 \u0628\u0631\u0627 \u0627\u0639\u0645\u0627\u0644 \u0634\u0648\u062f\u061b \u0628\u0631\u0627\u06cc\u06cc \u062f\u06cc\u06af\u0631 \u062d\u0627\u0635\u0644 \u0645\u06cc \u0634\u0648\u062f. \u062f\u0631 \u0641\u0636\u0627\u06cc \u06af\u0633\u0633\u062a\u0647 \u0648 \u0646\u0645\u0627\u06cc\u0634 \u0645\u0627\u062a\u0631\u06cc\u0633\u06cc\u060c \u0645\u0639\u0645\u0648\u0644\u0627 \u0639\u0645\u0644\u06af\u0631\u0647\u0627 \u0631\u0627 \u0628\u0627 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0647\u0627\u06cc \u0645\u0631\u0628\u0639\u06cc \u0646\u0645\u0627\u06cc\u0634 \u0645\u06cc \u062f\u0647\u06cc\u0645. \u0647\u0645\u0686\u0646\u06cc\u0646 \u0627\u063a\u0644\u0628 \u0639\u0645\u0644\u06af\u0631\u0647\u0627 \u062f\u0631 \u0645\u06a9\u0627\u0646\u06cc\u06a9 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645\u06cc\u060c \u0628\u0627 \u062d\u0631\u0648\u0641 \u0628\u0632\u0631\u06af \u0644\u0627\u062a\u06cc\u0646 \u0646\u0627\u0645\u06af\u0630\u0627\u0631\u06cc \u0645\u06cc \u0634\u0648\u0646\u062f \u0648 \u06af\u0627\u0647\u0627 \u06cc\u06a9 \u06a9\u0644\u0627\u0647 \u0628\u0631 \u0633\u0631\u062f\u0627\u0631\u0646\u062f. \u0639\u0645\u0644\u06af\u0631 $\\hat{A}$ \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u062f:<\/p>\n

(1)<\/strong><\/p>\n

$\\large \\hat{A}|\\psi \\rangle=|\\psi’ \\rangle\\; , \\; \\langle \\phi|\\hat{A}=\\langle \\phi’|$<\/p>\n

\u0627\u06af\u0631 \u0639\u0645\u0644\u06af\u0631 $\\hat{A}$ \u06cc\u06a9 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0645\u0631\u0628\u0639\u06cc \u0628\u0627 \u0645\u0631\u062a\u0628\u0647 \u0627\u06cc \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u062a\u0639\u062f\u0627\u062f \u062f\u0631\u0627\u06cc\u0647 \u0647\u0627\u06cc \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc \u062d\u0627\u0644\u062a (\u0686\u0647 \u06a9\u062a \u0648 \u0686\u0647 \u0628\u0631\u0627) \u0628\u0627\u0634\u062f\u061b \u062a\u0646\u0647\u0627 \u062f\u0631\u0635\u0648\u0631\u062a\u06cc \u0628\u0627\u0644\u0627 \u0636\u0631\u0628 \u0645\u0627\u062a\u0631\u06cc\u0633\u06cc \u0642\u0627\u0628\u0644 \u062a\u0639\u0631\u06cc\u0641 \u0627\u0633\u062a.<\/p>\n

\u0628\u0647 \u0637\u0648\u0631 \u0645\u0634\u0627\u0628\u0647 \u062a\u0639\u0631\u06cc\u0641 \u0628\u0627\u0644\u0627 \u0628\u0631\u0627\u06cc \u062a\u0648\u0627\u0628\u0639 \u0645\u0648\u062c \u0646\u06cc\u0632 \u0628\u0647 \u06a9\u0627\u0631 \u0645\u06cc \u0631\u0648\u062f:<\/p>\n

(2)<\/strong><\/p>\n

$\\large \\hat{A}\\psi(\\vec{r})=\\psi'(\\vec{r})\\; , \\; \\phi(\\vec{r})\\hat{A}=\\phi'(\\vec{r})$<\/p>\n

2-5 \u0686\u0646\u062f \u0639\u0645\u0644\u06af\u0631 \u062e\u0627\u0635<\/h3>\n

\u0639\u0645\u0644\u06af\u0631 \u06cc\u06a9\u0647<\/strong> $\\hat{I}$\u060c \u0639\u0645\u0644\u06af\u0631\u06cc \u06a9\u0647 \u062f\u0631 \u0635\u0648\u0631\u062a \u0627\u062b\u0631 \u0628\u0631 \u06a9\u062a\u060c \u0647\u0645\u0627\u0646 \u06a9\u062a \u0631\u0627 \u0646\u062a\u06cc\u062c\u0647 \u0645\u06cc \u062f\u0647\u062f:<\/p>\n

(3)<\/strong><\/p>\n

$\\large \\hat{I}|\\psi \\rangle=|\\psi \\rangle$<\/p>\n

\u0639\u0645\u0644\u06af\u0631 \u06af\u0631\u0627\u062f\u06cc\u0627\u0646 <\/strong>$\\nabla$\u060c \u0627\u0632 \u062a\u0627\u0628\u0639 \u0645\u0648\u062c\u060c \u0645\u0634\u062a\u0642 \u067e\u0627\u0631\u0647 \u0627\u06cc \u0628\u0631 \u062d\u0633\u0628 \u0645\u0648\u0644\u0641\u0647 \u0647\u0627\u06cc \u0641\u0636\u0627 \u0645\u06cc \u06af\u06cc\u0631\u062f \u0648 \u06cc\u06a9 \u0628\u0631\u062f\u0627\u0631 \u062e\u0631\u0648\u062c\u06cc \u0645\u06cc \u062f\u0647\u062f.<\/p>\n

(4)<\/strong><\/p>\n

$\\large \\nabla \\psi(\\vec{r})=\\displaystyle{\\frac{\\partial \\psi(\\vec{r})}{\\partial x}\\hat{i}+\\frac{\\partial \\psi(\\vec{r})}{\\partial y}\\hat{j}+\\frac{\\partial \\psi(\\vec{r})}{\\partial z}\\hat{k}}$<\/p>\n

\u062f\u0631 \u0631\u0627\u0628\u0637\u0647 \u0628\u0627\u0644\u0627\u060c $\\hat{j}$\u060c $\\hat{i}$ \u0648 $\\hat{k}$ \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc \u06cc\u06a9\u0647 \u0641\u0636\u0627\u06cc\u06cc \u062f\u0631 \u062c\u0647\u062a \u0633\u0647 \u0645\u062d\u0648\u0631 \u0645\u062e\u062a\u0635\u0627\u062a \u0647\u0633\u062a\u0646\u062f. \u0622\u0646 \u0647\u0627 \u0631\u0627 \u0628\u0627 \u0639\u0645\u0644\u06af\u0631 \u0627\u0634\u062a\u0628\u0627\u0647 \u0646\u06af\u06cc\u0631\u06cc\u062f.<\/p>\n

\u0639\u0645\u0644\u06af\u0631 \u062a\u06a9\u0627\u0646\u0647 \u062e\u0637\u06cc<\/strong> $\\hat{P}$\u060c \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc \u0634\u0648\u062f:<\/p>\n

(5)<\/strong><\/p>\n

$\\large \\hat{P}\\psi(\\vec{r})=-i\\hbar \\nabla \\psi(\\vec{r})$<\/p>\n

\u0639\u0645\u0644\u06af\u0631 \u0644\u0627\u067e\u0644\u0627\u0633\u06cc<\/strong> $\\nabla^2$\u060c \u0645\u062c\u0645\u0648\u0639 \u0645\u0634\u062a\u0642\u0627\u062a \u067e\u0627\u0631\u0647 \u0627\u06cc \u0645\u0631\u062a\u0628\u0647 \u062f\u0648\u0645 \u062a\u0627\u0628\u0639 \u0645\u0648\u062c \u0627\u0633\u062a:<\/p>\n

(6)<\/strong><\/p>\n

$\\large \\nabla^2 \\psi(\\vec{r})=\\displaystyle{\\frac{\\partial^2 \\psi(\\vec{r})}{\\partial x^2}\\hat{i}+\\frac{\\partial^2 \\psi(\\vec{r})}{\\partial y^2}\\hat{j}+\\frac{\\partial^2 \\psi(\\vec{r})}{\\partial z^2}\\hat{k}}$<\/p>\n

\u0639\u0645\u0644\u06af\u0631 \u067e\u0627\u0631\u06cc\u062a\u0647<\/strong> $\\mathcal{P}$\u060c \u0628\u0631\u062f\u0627\u0631 \u0645\u06a9\u0627\u0646 \u0631\u0627 \u0628\u0627 \u0642\u0631\u06cc\u0646\u0647 \u0627\u0634 \u062f\u0631 \u062a\u0627\u0628\u0639 \u0645\u0648\u062c \u062c\u0627\u06cc\u06af\u0632\u06cc\u0646 \u0645\u06cc \u06a9\u0646\u062f:<\/p>\n

(7)<\/strong><\/p>\n

$\\large \\mathcal{P}\\psi(\\vec{r})=\\psi(-\\vec{r})$<\/p>\n

3-5 \u0636\u0631\u0628 \u0639\u0645\u0644\u06af\u0631\u0647\u0627<\/h3>\n

\u0628\u0647 \u0637\u0648\u0631 \u06a9\u0644\u06cc\u060c \u0628\u0631\u0627\u06cc \u062f\u0648 \u0639\u0645\u0644\u06af\u0631 \u062f\u0644\u062e\u0648\u0627\u0647 $\\hat{A}$ \u0648 $\\hat{B}$\u060c \u0636\u0631\u0628 \u0639\u0645\u0644\u06cc \u062c\u0627\u0628\u062c\u0627\u067e\u0630\u06cc\u0631 \u0646\u06cc\u0633\u062a:<\/p>\n

(8)<\/strong><\/p>\n

$\\large \\hat{A}\\hat{B} \\neq \\hat{B}\\hat{A}$<\/p>\n

\u062e\u0627\u0635\u06cc\u062a \u0634\u0631\u06a9\u062a \u067e\u0630\u06cc\u0631\u06cc \u062f\u0631 \u0636\u0631\u0628 \u0639\u0645\u0644\u06af\u0631\u0647\u0627 \u0628\u0631\u0642\u0631\u0627\u0631 \u0627\u0633\u062a:<\/p>\n

(9)<\/strong><\/p>\n

$\\large \\hat{A}\\hat{B}\\hat{C}=(\\hat{A}\\hat{B})\\hat{C}=\\hat{A}(\\hat{B}\\hat{C})$<\/p>\n

\u0647\u0645\u0686\u0646\u06cc\u0646 \u0645\u06cc \u062a\u0648\u0627\u0646 \u062a\u0648\u0627\u0646 \u0647\u0627 \u0631\u0627 \u0628\u0627 \u0647\u0645 \u062c\u0645\u0639 \u06a9\u0631\u062f:<\/p>\n

(10)<\/strong><\/p>\n

$\\large \\hat{A}^n \\hat{A}^m = \\hat{A}^{n+m}$<\/p>\n

\u0647\u0646\u06af\u0627\u0645\u06cc \u06a9\u0647 \u0636\u0631\u0628 $\\hat{A}\\hat{B}$ \u0628\u0631 \u06a9\u062a \u062f\u0644\u062e\u0648\u0627\u0647 $| \\psi \\rangle $ \u0627\u062b\u0631 \u0645\u06cc \u06a9\u0646\u062f\u061b \u062a\u0631\u062a\u06cc\u0628 \u0639\u0645\u0644\u06af\u0631\u0647\u0627 \u062d\u0627\u0626\u0632 \u0627\u0647\u0645\u06cc\u062a \u0627\u0633\u062a. \u0647\u0645\u06cc\u0634\u0647 \u0627\u0632 \u0646\u0632\u062f\u06cc\u06a9\u062a\u0631\u06cc\u0646 \u0639\u0645\u0644\u06af\u0631\u060c \u0634\u0631\u0648\u0639 \u0628\u0647 \u0627\u062b\u0631 \u062f\u0627\u062f\u0646 \u0639\u0645\u0644\u06af\u0631\u0647\u0627 \u0645\u06cc \u06a9\u0646\u06cc\u0645. \u06cc\u0639\u0646\u06cc $\\hat{B}$ \u0646\u062e\u0633\u062a \u0628\u0631 $| \\psi \\rangle $ \u0627\u062b\u0631 \u0645\u06cc \u06a9\u0646\u062f\u061b \u0633\u067e\u0633 $\\hat{A}$ \u0631\u0627 \u0628\u0631 \u06a9\u062a \u062d\u0627\u0635\u0644 $\\hat{B} | \\psi \\rangle$ \u0627\u0639\u0645\u0627\u0644 \u0645\u06cc \u06a9\u0646\u06cc\u0645. \u0627\u06cc\u0646 \u0642\u0627\u0639\u062f\u0647 \u062f\u0631 \u0647\u0631\u062a\u0639\u062f\u0627\u062f \u0639\u0645\u0644\u06af\u0631 \u0636\u0631\u0628\u06cc \u0635\u0627\u062f\u0642 \u0627\u0633\u062a.<\/p>\n

(11)<\/strong><\/p>\n

$\\large \\hat{A}\\hat{B}| \\psi \\rangle=\\hat{A}(\\hat{B}| \\psi \\rangle)$<\/p>\n

\u062f\u0631 \u0635\u0648\u0631\u062a\u06cc \u06a9\u0647 \u0639\u0645\u0644\u06af\u0631 $\\hat{A}$\u060c \u0628\u06cc\u0646 \u06cc\u06a9 \u0628\u0631\u0627 $\\langle \\phi |$\u00a0 \u0648 \u06cc\u06a9 \u06a9\u062a $| \\psi \\rangle $ \u0642\u0631\u0627\u0631 \u0628\u06af\u06cc\u0631\u062f\u061b \u062d\u0627\u0635\u0644 \u06cc\u06a9 \u0639\u062f\u062f \u0645\u062e\u062a\u0644\u0637 (\u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u062d\u0642\u06cc\u0642\u06cc \u06cc\u0627 \u0645\u0648\u0647\u0648\u0645\u06cc \u0645\u062d\u0636 \u0646\u06cc\u0632 \u0628\u0627\u0634\u062f) \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f. \u062a\u0648\u062c\u0647 \u0628\u0647 \u0636\u0631\u0628 \u0645\u0627\u062a\u0631\u06cc\u0633\u06cc\u060c \u06cc\u06a9 \u0628\u0631\u062f\u0627\u0631 \u0633\u0637\u0631\u06cc \u062f\u0631 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0645\u0631\u0628\u0639\u06cc \u062f\u0631 \u06cc\u06a9 \u0628\u0631\u062f\u0627\u0631 \u0633\u062a\u0648\u0646\u06cc\u060c \u0646\u062a\u06cc\u062c\u0647 \u06af\u06cc\u0631\u06cc \u0631\u0627 \u0633\u0627\u062f\u0647 \u0645\u06cc \u06a9\u0646\u062f.<\/p>\n

(12)<\/strong><\/p>\n

$\\large \\langle \\phi | \\hat{A} | \\psi \\rangle =$ \u0639\u062f\u062f \u0645\u062e\u062a\u0644\u0637<\/h5>\n

\u0647\u0645\u0686\u0646\u06cc\u0646 \u0627\u0647\u0645\u06cc\u062a\u06cc \u0646\u062f\u0627\u0631\u062f \u06a9\u0647 \u0639\u0645\u0644\u06af\u0631\u060c \u0627\u0628\u062a\u062f\u0627 \u0628\u0631 \u0628\u0631\u0627 \u0627\u062b\u0631 \u06a9\u0646\u062f \u0648 \u0633\u067e\u0633 \u0628\u0631\u0627\u06cc \u062d\u0627\u0635\u0644 \u062f\u0631 \u06a9\u062a \u0636\u0631\u0628 \u0634\u0648\u062f \u06cc\u0627 \u0627\u0628\u062a\u062f\u0627 \u0628\u0631 \u06a9\u062a \u0627\u062b\u0631 \u06a9\u0646\u062f\u060c \u0633\u067e\u0633 \u06a9\u062a \u062d\u0627\u0635\u0644 \u062f\u0631 \u0628\u0631\u0627 \u0636\u0631\u0628 \u0634\u0648\u062f:<\/p>\n

(13)<\/strong><\/p>\n

$\\large (\\: \\langle \\phi | \\hat{A} \\: ) \\: | \\psi \\rangle = \\langle \\phi | \\: (\\: \\hat{A} | \\psi \\rangle \\: )$<\/p>\n

4-5 \u0639\u0645\u0644\u06af\u0631 \u062e\u0637\u06cc<\/h3>\n

\u0639\u0645\u0644\u06af\u0631 $\\hat{A}$ \u062f\u0631 \u0635\u0648\u0631\u062a\u06cc \u062e\u0637\u06cc \u0646\u0627\u0645\u06cc\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f \u06a9\u0647 \u062f\u0627\u0631\u0627\u06cc \u062e\u0627\u0635\u06cc\u062a \u062a\u0648\u0632\u06cc\u0639 \u067e\u0630\u06cc\u0631\u06cc (\u067e\u062e\u0634 \u067e\u0630\u06cc\u0631\u06cc) \u0628\u0627\u0634\u062f \u0648 \u062b\u0627\u0628\u062a \u0647\u0627\u06cc \u0639\u062f\u062f\u06cc \u062c\u0627\u0628\u062c\u0627 \u0634\u0648\u062f. \u0635\u0648\u0631\u062a \u0646\u0645\u0627\u062f\u06cc\u0646 \u062c\u0645\u0644\u0647 \u0642\u0628\u0644 \u0631\u0627 \u062f\u0631 \u062f\u0648 \u0631\u0627\u0628\u0637\u0647 \u067e\u0627\u06cc\u06cc\u0646 \u0628\u0631\u0627\u06cc \u06a9\u062a \u0647\u0627 $| \\psi_i \\rangle$ \u060c \u0628\u0631\u0627\u0647\u0627 $ \\langle \\phi_i |$ \u0648 \u0627\u0639\u062f\u0627\u062f \u0645\u062e\u062a\u0644\u0637 $a_i$ \u062f\u0644\u062e\u0648\u0627\u0647 \u0622\u0648\u0631\u062f\u0647 \u0627\u0645:<\/p>\n

(14)<\/strong><\/p>\n

$\\large \\hat{A}(a_1|\\psi_1 \\rangle+a_2|\\psi_2 \\rangle)=a_1\\hat{A}|\\psi_1 \\rangle+a_2\\hat{A}|\\psi_2 \\rangle$<\/p>\n

(15)<\/strong><\/p>\n

$\\large (\\langle\\phi_1|a_1+\\langle\\phi_2|a_2)\\hat{A}=a_1\\langle\\phi_1|\\hat{A}+a_2\\langle\\phi_2|\\hat{A}$<\/p>\n

5-5 \u0645\u0642\u062f\u0627\u0631 \u0686\u0634\u0645\u062f\u0627\u0634\u062a\u06cc<\/h3>\n

\u0645\u0642\u062f\u0627\u0631 \u0686\u0634\u0645\u062f\u0627\u0634\u062a\u06cc \u06cc\u0627 \u0645\u06cc\u0627\u0646\u06af\u06cc\u0646 \u0639\u0645\u0644\u06af\u0631 $\\hat{A}$ \u0646\u0633\u0628\u062a \u0628\u0647 \u062d\u0627\u0644\u062a $|\\psi \\rangle$\u060c \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc \u0634\u0648\u062f:<\/p>\n

(16)<\/strong><\/p>\n

$\\large \\langle \\hat{A} \\rangle = \\displaystyle{\\frac{\\langle \\psi | \\hat{A} | \\psi \\rangle}{\\langle \\psi | \\psi \\rangle}}$<\/p>\n

\u0648\u0627\u0636\u062d \u0627\u0633\u062a \u06a9\u0647 \u0627\u06af\u0631 \u062d\u0627\u0644\u062a $|\\psi \\rangle$ \u0628\u0647\u0646\u062c\u0627\u0631 \u0628\u0627\u0634\u062f\u061b \u0645\u062e\u0631\u062c \u0631\u0627\u0628\u0637\u0647 \u0628\u0627\u0644\u0627 \u06cc\u06a9 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f.<\/p>\n

6-5 \u0645\u0644\u0627\u062d\u0638\u0627\u062a<\/h3>\n
    \n
  • \u0636\u0631\u0628 \u06cc\u06a9 \u06a9\u062a \u062f\u0631 \u06cc\u06a9 \u0628\u0631\u0627 $|\\phi\\rangle\\langle \\psi|$ \u06cc\u06a9 \u0639\u0645\u0644\u06af\u0631 \u062e\u0637\u06cc \u0627\u0633\u062a. \u0627\u0632 \u0627\u06cc\u0646 \u0646\u0638\u0631 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0639\u0645\u0644\u06af\u0631 \u0628\u0648\u062f\u0646 \u0622\u0646 \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u06a9\u0631\u062f \u06a9\u0647 \u062f\u0631 \u0635\u0648\u0631\u062a\u06cc \u06a9\u0647 \u0628\u0631 \u06cc\u06a9 \u06a9\u062a \u062f\u0644\u062e\u0648\u0627\u0647 $| \\psi’ \\rangle$ \u0627\u0639\u0645\u0627\u0644 \u0634\u0648\u062f\u061b \u06a9\u062a \u062f\u06cc\u06af\u0631\u06cc \u0631\u0627 \u0646\u062a\u06cc\u062c\u0647 \u0645\u06cc \u062f\u0647\u062f:<\/li>\n<\/ul>\n

    (17)<\/strong><\/p>\n

    $\\large (|\\phi\\rangle\\langle \\psi|)| \\psi’ \\rangle = (\\langle \\psi | \\psi’ \\rangle) |\\phi\\rangle$<\/p>\n

    \u06a9\u0647 $\\langle \\psi | \\psi’ \\rangle$ \u06cc\u06a9 \u0639\u062f\u062f \u0645\u062e\u062a\u0644\u0637 \u0627\u0633\u062a.<\/p>\n

      \n
    • \u0636\u0631\u0628 \u06cc\u06a9 \u0639\u0645\u0644\u06af\u0631 \u0627\u0632 \u0686\u067e \u062f\u0631 \u06cc\u06a9 \u0628\u0631\u0627 $\\hat{A}\\langle \\phi |$ \u0648 \u0636\u0631\u0628 \u06cc\u06a9 \u0639\u0645\u0644\u06af\u0631 \u0627\u0632 \u0631\u0627\u0633\u062a \u062f\u0631 \u06cc\u06a9 \u06a9\u062a $ |\\psi \\rangle\\hat{A}$ \u0645\u0639\u0646\u0627\u06cc\u06cc \u0646\u062f\u0627\u0631\u062f. \u0639\u0644\u062a \u0622\u0646 \u0627\u0632 \u0636\u0631\u0628 \u0645\u0627\u062a\u0631\u06cc\u0633\u06cc\u060c \u0628\u0627 \u062f\u0631 \u0646\u0638\u0631 \u06af\u0631\u0641\u062a\u0646 \u0628\u0631\u0627 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0628\u0631\u062f\u0627\u0631 \u0633\u0637\u0631\u06cc \u0648 \u06a9\u062a \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0628\u0631\u062f\u0627\u0631 \u0633\u062a\u0648\u0646\u06cc\u060c \u0628\u0648\u0636\u0648\u062d \u0645\u0634\u062e\u0635 \u0627\u0633\u062a.<\/li>\n<\/ul>\n

      7-5 \u062c\u0645\u0639 \u0628\u0646\u062f\u06cc \u0641\u0635\u0644<\/h3>\n

      \u062f\u0631 \u0627\u06cc\u0646 \u0641\u0635\u0644 \u0628\u0637\u0648\u0631 \u0639\u0645\u0648\u0645\u06cc \u0628\u0627 \u0639\u0645\u0644\u06af\u0631 \u0622\u0634\u0646\u0627 \u0634\u062f\u06cc\u0645 \u0648 \u062e\u0648\u0627\u0635 \u0622\u0646 \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u06a9\u0631\u062f\u06cc\u0645. \u0647\u0645\u0686\u0646\u06cc\u0646 \u0628\u0647 \u0646\u062d\u0648\u0647 \u0636\u0631\u0628 \u0639\u0645\u0644\u06af\u0631\u0647\u0627\u060c \u062a\u0639\u0631\u06cc\u0641 \u0639\u0645\u0644\u06af\u0631 \u062e\u0637\u06cc \u0648 \u0645\u0642\u062f\u0627\u0631 \u0686\u0634\u0645\u062f\u0627\u0634\u062a\u06cc \u0646\u06cc\u0632 \u067e\u0631\u062f\u0627\u062e\u062a\u06cc\u0645.<\/p>\n

       <\/p>\n\n\n\n
      \u062a\u0645\u0631\u06cc\u0646\u0627\u062a \u0641\u0635\u0644<\/span><\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      *1- \u0639\u0645\u0644\u06af\u0631 \u0645\u0627\u062a\u0631\u06cc\u0633\u06cc $S_x$ \u0631\u0627 \u062f\u0631\u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u062f:<\/p>\n

      $\\large S_x=\\displaystyle{\\frac{\\hbar}{2}\\begin{bmatrix} 0 & 1\\\\ 1 & 0 \\end{bmatrix}}$<\/p>\n

      \u0645\u0642\u062f\u0627\u0631 \u0686\u0634\u0645\u062f\u0627\u0634\u062a\u06cc $\\langle S_x \\rangle$ \u0631\u0627 \u062f\u0631 \u062d\u0627\u0644\u062a $| \\psi \\rangle$ \u0628\u062f\u0633\u062a \u0622\u0648\u0631\u06cc\u062f:<\/p>\n

      $| \\psi \\rangle=\\displaystyle{\\begin{bmatrix} 1\\\\ 1+3i \\end{bmatrix}}$<\/p>\n","protected":false},"excerpt":{"rendered":"

      \u06cc\u06a9\u06cc \u0627\u0632 \u0645\u0641\u0627\u0647\u06cc\u0645 \u0628\u0646\u06cc\u0627\u062f\u06cc \u062f\u0631 \u0635\u0648\u0631\u062a \u0628\u0646\u062f\u06cc \u0645\u06a9\u0627\u0646\u06cc\u06a9 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645\u06cc\u060c \u0639\u0645\u0644\u06af\u0631 \u0627\u0633\u062a. \u062f\u0631 \u0627\u06cc\u0646 \u0641\u0635\u0644 \u0628\u0627 \u062a\u0639\u0631\u06cc\u0641 \u0639\u0645\u0644\u06af\u0631 \u0648 \u0686\u0646\u062f \u0639\u0645\u0644\u06af\u0631 \u062e\u0627\u0635 \u06a9\u0647 \u062f\u0631 \u0645\u06a9\u0627\u0646\u06cc\u06a9 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645 \u06a9\u0627\u0631\u0628\u0631\u062f \u062f\u0627\u0631\u0646\u062f\u061b \u0622\u0634\u0646\u0627 \u0645\u06cc \u0634\u0648\u06cc\u0645. 1-5 \u062a\u0639\u0631\u06cc\u0641 \u0639\u0645\u0644\u06af\u0631 \u0642\u0627\u0639\u062f\u0647 \u0627\u06cc \u0631\u06cc\u0627\u0636\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0627\u06af\u0631 \u0628\u0631 \u06cc\u06a9 \u0628\u0631\u062f\u0627\u0631\u062d\u0627\u0644\u062a \u06a9\u062a \u0627\u0639\u0645\u0627\u0644 \u0634\u0648\u062f\u060c \u06a9\u062a \u062f\u06cc\u06af\u0631\u06cc \u0646\u062a\u06cc\u062c\u0647 \u0645\u06cc \u062f\u0647\u062f \u0648 \u0627\u06af\u0631 \u0628\u0631 \u06cc\u06a9 \u0628\u0631\u0627 […]<\/p>\n","protected":false},"author":1,"featured_media":307,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"https:\/\/cdn.imgurl.ir\/uploads\/i9737_screenshot_2023-08-22_055539_r0u.png","fifu_image_alt":"\u0639\u0645\u0644\u06af\u0631","footnotes":""},"categories":[5,26],"tags":[28,27],"class_list":["post-306","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-physics","category-26","tag-28","tag-27"],"yoast_head":"\n5 \u0639\u0645\u0644\u06af\u0631 : \u0645\u0642\u062f\u0645\u0647 - \u0633\u0627\u06cc\u0646\u0633\u06cc\u0648<\/title>\n<meta name=\"description\" content=\"\u0639\u0645\u0644\u06af\u0631 \u06cc\u06a9\u06cc \u0627\u0632 \u0645\u0641\u0627\u0647\u06cc\u0645 \u0628\u0646\u06cc\u0627\u062f\u06cc \u062f\u0631 \u0635\u0648\u0631\u062a\u0628\u0646\u062f\u06cc \u0645\u06a9\u0627\u0646\u06cc\u06a9 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645\u06cc \u0627\u0633\u062a. \u0628\u0627 \u062a\u0639\u0631\u06cc\u0641 \u0686\u0646\u062f \u0639\u0645\u0644\u06af\u0631 \u062e\u0627\u0635 \u06a9\u0647 \u062f\u0631 \u0645\u06a9\u0627\u0646\u06cc\u06a9 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645 \u06a9\u0627\u0631\u0628\u0631\u062f \u062f\u0627\u0631\u0646\u062f \u0622\u0634\u0646\u0627 \u0645\u06cc \u0634\u0648\u06cc\u0645.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/sciencio.ir\/?p=306\" \/>\n<meta property=\"og:locale\" content=\"fa_IR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"5 \u0639\u0645\u0644\u06af\u0631 : \u0645\u0642\u062f\u0645\u0647 - \u0633\u0627\u06cc\u0646\u0633\u06cc\u0648\" \/>\n<meta property=\"og:description\" content=\"\u0639\u0645\u0644\u06af\u0631 \u06cc\u06a9\u06cc \u0627\u0632 \u0645\u0641\u0627\u0647\u06cc\u0645 \u0628\u0646\u06cc\u0627\u062f\u06cc \u062f\u0631 \u0635\u0648\u0631\u062a\u0628\u0646\u062f\u06cc \u0645\u06a9\u0627\u0646\u06cc\u06a9 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645\u06cc \u0627\u0633\u062a. \u0628\u0627 \u062a\u0639\u0631\u06cc\u0641 \u0686\u0646\u062f \u0639\u0645\u0644\u06af\u0631 \u062e\u0627\u0635 \u06a9\u0647 \u062f\u0631 \u0645\u06a9\u0627\u0646\u06cc\u06a9 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645 \u06a9\u0627\u0631\u0628\u0631\u062f \u062f\u0627\u0631\u0646\u062f \u0622\u0634\u0646\u0627 \u0645\u06cc \u0634\u0648\u06cc\u0645.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/sciencio.ir\/?p=306\" \/>\n<meta property=\"og:site_name\" content=\"\u0633\u0627\u06cc\u0646\u0633\u06cc\u0648\" \/>\n<meta property=\"article:published_time\" content=\"2026-08-12T04:08:54+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-08-12T04:11:59+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/cdn.imgurl.ir\/uploads\/i9737_screenshot_2023-08-22_055539_r0u.png\" \/>\n\t<meta property=\"og:image:width\" content=\"950\" \/>\n\t<meta property=\"og:image:height\" content=\"558\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"sciencio\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u0646\u0648\u0634\u062a\u0647\u200c\u0634\u062f\u0647 \u0628\u062f\u0633\u062a\" \/>\n\t<meta name=\"twitter:data1\" content=\"sciencio\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u0632\u0645\u0627\u0646 \u062a\u0642\u0631\u06cc\u0628\u06cc \u0628\u0631\u0627\u06cc \u062e\u0648\u0627\u0646\u062f\u0646\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 \u062f\u0642\u06cc\u0642\u0647\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/sciencio.ir\\\/?p=306#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/sciencio.ir\\\/?p=306\"},\"author\":{\"name\":\"sciencio\",\"@id\":\"https:\\\/\\\/sciencio.ir\\\/#\\\/schema\\\/person\\\/2b2180aaa7b9d8f01859dce0c2ce52fb\"},\"headline\":\"5 \u0639\u0645\u0644\u06af\u0631 : \u0645\u0642\u062f\u0645\u0647\",\"datePublished\":\"2026-08-12T04:08:54+00:00\",\"dateModified\":\"2026-08-12T04:11:59+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/sciencio.ir\\\/?p=306\"},\"wordCount\":381,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\\\/\\\/sciencio.ir\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/sciencio.ir\\\/?p=306#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/cdn.imgurl.ir\\\/uploads\\\/i9737_screenshot_2023-08-22_055539_r0u.png\",\"keywords\":[\"\u0628\u062e\u0634 \u0645\u0642\u062f\u0645\u0627\u062a\u06cc (\u0645\u06a9\u0627\u0646\u06cc\u06a9 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645\u06cc)\",\"\u06a9\u062a\u0627\u0628 \u0645\u06a9\u0627\u0646\u06cc\u06a9 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645\u06cc\"],\"articleSection\":[\"\u0641\u06cc\u0632\u06cc\u06a9\",\"\u0645\u06a9\u0627\u0646\u06cc\u06a9 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645\u06cc\"],\"inLanguage\":\"fa-IR\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/sciencio.ir\\\/?p=306#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/sciencio.ir\\\/?p=306\",\"url\":\"https:\\\/\\\/sciencio.ir\\\/?p=306\",\"name\":\"5 \u0639\u0645\u0644\u06af\u0631 : \u0645\u0642\u062f\u0645\u0647 - \u0633\u0627\u06cc\u0646\u0633\u06cc\u0648\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/sciencio.ir\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/sciencio.ir\\\/?p=306#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/sciencio.ir\\\/?p=306#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/cdn.imgurl.ir\\\/uploads\\\/i9737_screenshot_2023-08-22_055539_r0u.png\",\"datePublished\":\"2026-08-12T04:08:54+00:00\",\"dateModified\":\"2026-08-12T04:11:59+00:00\",\"description\":\"\u0639\u0645\u0644\u06af\u0631 \u06cc\u06a9\u06cc \u0627\u0632 \u0645\u0641\u0627\u0647\u06cc\u0645 \u0628\u0646\u06cc\u0627\u062f\u06cc \u062f\u0631 \u0635\u0648\u0631\u062a\u0628\u0646\u062f\u06cc \u0645\u06a9\u0627\u0646\u06cc\u06a9 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645\u06cc \u0627\u0633\u062a. \u0628\u0627 \u062a\u0639\u0631\u06cc\u0641 \u0686\u0646\u062f \u0639\u0645\u0644\u06af\u0631 \u062e\u0627\u0635 \u06a9\u0647 \u062f\u0631 \u0645\u06a9\u0627\u0646\u06cc\u06a9 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645 \u06a9\u0627\u0631\u0628\u0631\u062f \u062f\u0627\u0631\u0646\u062f \u0622\u0634\u0646\u0627 \u0645\u06cc \u0634\u0648\u06cc\u0645.\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/sciencio.ir\\\/?p=306#breadcrumb\"},\"inLanguage\":\"fa-IR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/sciencio.ir\\\/?p=306\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"fa-IR\",\"@id\":\"https:\\\/\\\/sciencio.ir\\\/?p=306#primaryimage\",\"url\":\"https:\\\/\\\/cdn.imgurl.ir\\\/uploads\\\/i9737_screenshot_2023-08-22_055539_r0u.png\",\"contentUrl\":\"https:\\\/\\\/cdn.imgurl.ir\\\/uploads\\\/i9737_screenshot_2023-08-22_055539_r0u.png\",\"width\":950,\"height\":558,\"caption\":\"\u0639\u0645\u0644\u06af\u0631\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/sciencio.ir\\\/?p=306#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/sciencio.ir\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"5 \u0639\u0645\u0644\u06af\u0631 : \u0645\u0642\u062f\u0645\u0647\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/sciencio.ir\\\/#website\",\"url\":\"https:\\\/\\\/sciencio.ir\\\/\",\"name\":\"\u0633\u0627\u06cc\u0646\u0633\u06cc\u0648\",\"description\":\"\u062f\u0627\u0646\u0634 \u062f\u0648\u0633\u062a \u062f\u0627\u0634\u062a\u0646\u06cc!\",\"publisher\":{\"@id\":\"https:\\\/\\\/sciencio.ir\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/sciencio.ir\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"fa-IR\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/sciencio.ir\\\/#organization\",\"name\":\"\u0633\u0627\u06cc\u0646\u0633\u06cc\u0648\",\"url\":\"https:\\\/\\\/sciencio.ir\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"fa-IR\",\"@id\":\"https:\\\/\\\/sciencio.ir\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"http:\\\/\\\/sciencio.ir\\\/wp-content\\\/uploads\\\/2026\\\/06\\\/sciencic.png\",\"contentUrl\":\"http:\\\/\\\/sciencio.ir\\\/wp-content\\\/uploads\\\/2026\\\/06\\\/sciencic.png\",\"width\":1080,\"height\":1080,\"caption\":\"\u0633\u0627\u06cc\u0646\u0633\u06cc\u0648\"},\"image\":{\"@id\":\"https:\\\/\\\/sciencio.ir\\\/#\\\/schema\\\/logo\\\/image\\\/\"}},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/sciencio.ir\\\/#\\\/schema\\\/person\\\/2b2180aaa7b9d8f01859dce0c2ce52fb\",\"name\":\"sciencio\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"fa-IR\",\"@id\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/2ff6c8ff49a0012472a4cf0c4c2c0978b9725facc1cd4b1177c68cac052ac852?s=96&d=mm&r=g\",\"url\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/2ff6c8ff49a0012472a4cf0c4c2c0978b9725facc1cd4b1177c68cac052ac852?s=96&d=mm&r=g\",\"contentUrl\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/2ff6c8ff49a0012472a4cf0c4c2c0978b9725facc1cd4b1177c68cac052ac852?s=96&d=mm&r=g\",\"caption\":\"sciencio\"},\"sameAs\":[\"http:\\\/\\\/sciencio.ir\"],\"url\":\"https:\\\/\\\/sciencio.ir\\\/?author=1\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"5 \u0639\u0645\u0644\u06af\u0631 : \u0645\u0642\u062f\u0645\u0647 - \u0633\u0627\u06cc\u0646\u0633\u06cc\u0648","description":"\u0639\u0645\u0644\u06af\u0631 \u06cc\u06a9\u06cc \u0627\u0632 \u0645\u0641\u0627\u0647\u06cc\u0645 \u0628\u0646\u06cc\u0627\u062f\u06cc \u062f\u0631 \u0635\u0648\u0631\u062a\u0628\u0646\u062f\u06cc \u0645\u06a9\u0627\u0646\u06cc\u06a9 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645\u06cc \u0627\u0633\u062a. \u0628\u0627 \u062a\u0639\u0631\u06cc\u0641 \u0686\u0646\u062f \u0639\u0645\u0644\u06af\u0631 \u062e\u0627\u0635 \u06a9\u0647 \u062f\u0631 \u0645\u06a9\u0627\u0646\u06cc\u06a9 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645 \u06a9\u0627\u0631\u0628\u0631\u062f \u062f\u0627\u0631\u0646\u062f \u0622\u0634\u0646\u0627 \u0645\u06cc \u0634\u0648\u06cc\u0645.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/sciencio.ir\/?p=306","og_locale":"fa_IR","og_type":"article","og_title":"5 \u0639\u0645\u0644\u06af\u0631 : \u0645\u0642\u062f\u0645\u0647 - \u0633\u0627\u06cc\u0646\u0633\u06cc\u0648","og_description":"\u0639\u0645\u0644\u06af\u0631 \u06cc\u06a9\u06cc \u0627\u0632 \u0645\u0641\u0627\u0647\u06cc\u0645 \u0628\u0646\u06cc\u0627\u062f\u06cc \u062f\u0631 \u0635\u0648\u0631\u062a\u0628\u0646\u062f\u06cc \u0645\u06a9\u0627\u0646\u06cc\u06a9 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645\u06cc \u0627\u0633\u062a. \u0628\u0627 \u062a\u0639\u0631\u06cc\u0641 \u0686\u0646\u062f \u0639\u0645\u0644\u06af\u0631 \u062e\u0627\u0635 \u06a9\u0647 \u062f\u0631 \u0645\u06a9\u0627\u0646\u06cc\u06a9 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645 \u06a9\u0627\u0631\u0628\u0631\u062f \u062f\u0627\u0631\u0646\u062f \u0622\u0634\u0646\u0627 \u0645\u06cc \u0634\u0648\u06cc\u0645.","og_url":"https:\/\/sciencio.ir\/?p=306","og_site_name":"\u0633\u0627\u06cc\u0646\u0633\u06cc\u0648","article_published_time":"2026-08-12T04:08:54+00:00","article_modified_time":"2026-08-12T04:11:59+00:00","og_image":[{"width":950,"height":558,"url":"https:\/\/cdn.imgurl.ir\/uploads\/i9737_screenshot_2023-08-22_055539_r0u.png","type":"image\/jpeg"}],"author":"sciencio","twitter_card":"summary_large_image","twitter_misc":{"\u0646\u0648\u0634\u062a\u0647\u200c\u0634\u062f\u0647 \u0628\u062f\u0633\u062a":"sciencio","\u0632\u0645\u0627\u0646 \u062a\u0642\u0631\u06cc\u0628\u06cc \u0628\u0631\u0627\u06cc \u062e\u0648\u0627\u0646\u062f\u0646":"5 \u062f\u0642\u06cc\u0642\u0647"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/sciencio.ir\/?p=306#article","isPartOf":{"@id":"https:\/\/sciencio.ir\/?p=306"},"author":{"name":"sciencio","@id":"https:\/\/sciencio.ir\/#\/schema\/person\/2b2180aaa7b9d8f01859dce0c2ce52fb"},"headline":"5 \u0639\u0645\u0644\u06af\u0631 : \u0645\u0642\u062f\u0645\u0647","datePublished":"2026-08-12T04:08:54+00:00","dateModified":"2026-08-12T04:11:59+00:00","mainEntityOfPage":{"@id":"https:\/\/sciencio.ir\/?p=306"},"wordCount":381,"commentCount":0,"publisher":{"@id":"https:\/\/sciencio.ir\/#organization"},"image":{"@id":"https:\/\/sciencio.ir\/?p=306#primaryimage"},"thumbnailUrl":"https:\/\/cdn.imgurl.ir\/uploads\/i9737_screenshot_2023-08-22_055539_r0u.png","keywords":["\u0628\u062e\u0634 \u0645\u0642\u062f\u0645\u0627\u062a\u06cc (\u0645\u06a9\u0627\u0646\u06cc\u06a9 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645\u06cc)","\u06a9\u062a\u0627\u0628 \u0645\u06a9\u0627\u0646\u06cc\u06a9 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645\u06cc"],"articleSection":["\u0641\u06cc\u0632\u06cc\u06a9","\u0645\u06a9\u0627\u0646\u06cc\u06a9 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645\u06cc"],"inLanguage":"fa-IR","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/sciencio.ir\/?p=306#respond"]}]},{"@type":"WebPage","@id":"https:\/\/sciencio.ir\/?p=306","url":"https:\/\/sciencio.ir\/?p=306","name":"5 \u0639\u0645\u0644\u06af\u0631 : \u0645\u0642\u062f\u0645\u0647 - \u0633\u0627\u06cc\u0646\u0633\u06cc\u0648","isPartOf":{"@id":"https:\/\/sciencio.ir\/#website"},"primaryImageOfPage":{"@id":"https:\/\/sciencio.ir\/?p=306#primaryimage"},"image":{"@id":"https:\/\/sciencio.ir\/?p=306#primaryimage"},"thumbnailUrl":"https:\/\/cdn.imgurl.ir\/uploads\/i9737_screenshot_2023-08-22_055539_r0u.png","datePublished":"2026-08-12T04:08:54+00:00","dateModified":"2026-08-12T04:11:59+00:00","description":"\u0639\u0645\u0644\u06af\u0631 \u06cc\u06a9\u06cc \u0627\u0632 \u0645\u0641\u0627\u0647\u06cc\u0645 \u0628\u0646\u06cc\u0627\u062f\u06cc \u062f\u0631 \u0635\u0648\u0631\u062a\u0628\u0646\u062f\u06cc \u0645\u06a9\u0627\u0646\u06cc\u06a9 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645\u06cc \u0627\u0633\u062a. \u0628\u0627 \u062a\u0639\u0631\u06cc\u0641 \u0686\u0646\u062f \u0639\u0645\u0644\u06af\u0631 \u062e\u0627\u0635 \u06a9\u0647 \u062f\u0631 \u0645\u06a9\u0627\u0646\u06cc\u06a9 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645 \u06a9\u0627\u0631\u0628\u0631\u062f \u062f\u0627\u0631\u0646\u062f \u0622\u0634\u0646\u0627 \u0645\u06cc \u0634\u0648\u06cc\u0645.","breadcrumb":{"@id":"https:\/\/sciencio.ir\/?p=306#breadcrumb"},"inLanguage":"fa-IR","potentialAction":[{"@type":"ReadAction","target":["https:\/\/sciencio.ir\/?p=306"]}]},{"@type":"ImageObject","inLanguage":"fa-IR","@id":"https:\/\/sciencio.ir\/?p=306#primaryimage","url":"https:\/\/cdn.imgurl.ir\/uploads\/i9737_screenshot_2023-08-22_055539_r0u.png","contentUrl":"https:\/\/cdn.imgurl.ir\/uploads\/i9737_screenshot_2023-08-22_055539_r0u.png","width":950,"height":558,"caption":"\u0639\u0645\u0644\u06af\u0631"},{"@type":"BreadcrumbList","@id":"https:\/\/sciencio.ir\/?p=306#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/sciencio.ir\/"},{"@type":"ListItem","position":2,"name":"5 \u0639\u0645\u0644\u06af\u0631 : \u0645\u0642\u062f\u0645\u0647"}]},{"@type":"WebSite","@id":"https:\/\/sciencio.ir\/#website","url":"https:\/\/sciencio.ir\/","name":"\u0633\u0627\u06cc\u0646\u0633\u06cc\u0648","description":"\u062f\u0627\u0646\u0634 \u062f\u0648\u0633\u062a \u062f\u0627\u0634\u062a\u0646\u06cc!","publisher":{"@id":"https:\/\/sciencio.ir\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/sciencio.ir\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"fa-IR"},{"@type":"Organization","@id":"https:\/\/sciencio.ir\/#organization","name":"\u0633\u0627\u06cc\u0646\u0633\u06cc\u0648","url":"https:\/\/sciencio.ir\/","logo":{"@type":"ImageObject","inLanguage":"fa-IR","@id":"https:\/\/sciencio.ir\/#\/schema\/logo\/image\/","url":"http:\/\/sciencio.ir\/wp-content\/uploads\/2026\/06\/sciencic.png","contentUrl":"http:\/\/sciencio.ir\/wp-content\/uploads\/2026\/06\/sciencic.png","width":1080,"height":1080,"caption":"\u0633\u0627\u06cc\u0646\u0633\u06cc\u0648"},"image":{"@id":"https:\/\/sciencio.ir\/#\/schema\/logo\/image\/"}},{"@type":"Person","@id":"https:\/\/sciencio.ir\/#\/schema\/person\/2b2180aaa7b9d8f01859dce0c2ce52fb","name":"sciencio","image":{"@type":"ImageObject","inLanguage":"fa-IR","@id":"https:\/\/secure.gravatar.com\/avatar\/2ff6c8ff49a0012472a4cf0c4c2c0978b9725facc1cd4b1177c68cac052ac852?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/2ff6c8ff49a0012472a4cf0c4c2c0978b9725facc1cd4b1177c68cac052ac852?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/2ff6c8ff49a0012472a4cf0c4c2c0978b9725facc1cd4b1177c68cac052ac852?s=96&d=mm&r=g","caption":"sciencio"},"sameAs":["http:\/\/sciencio.ir"],"url":"https:\/\/sciencio.ir\/?author=1"}]}},"_links":{"self":[{"href":"https:\/\/sciencio.ir\/index.php?rest_route=\/wp\/v2\/posts\/306","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sciencio.ir\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sciencio.ir\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sciencio.ir\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sciencio.ir\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=306"}],"version-history":[{"count":1,"href":"https:\/\/sciencio.ir\/index.php?rest_route=\/wp\/v2\/posts\/306\/revisions"}],"predecessor-version":[{"id":308,"href":"https:\/\/sciencio.ir\/index.php?rest_route=\/wp\/v2\/posts\/306\/revisions\/308"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/sciencio.ir\/index.php?rest_route=\/wp\/v2\/media\/307"}],"wp:attachment":[{"href":"https:\/\/sciencio.ir\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=306"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sciencio.ir\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=306"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sciencio.ir\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=306"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}