{"id":303,"date":"2026-08-12T07:36:33","date_gmt":"2026-08-12T04:06:33","guid":{"rendered":"https:\/\/sciencio.ir\/?p=303"},"modified":"2026-08-12T07:36:33","modified_gmt":"2026-08-12T04:06:33","slug":"4-%d9%86%d9%85%d8%a7%d8%af%da%af%d8%b0%d8%a7%d8%b1%db%8c-%d8%af%db%8c%d8%b1%d8%a7%da%a9","status":"publish","type":"post","link":"https:\/\/sciencio.ir\/?p=303","title":{"rendered":"4 \u0646\u0645\u0627\u062f\u06af\u0630\u0627\u0631\u06cc \u062f\u06cc\u0631\u0627\u06a9"},"content":{"rendered":"<p>\u062d\u0627\u0644\u062a \u0641\u06cc\u0632\u06cc\u06a9\u06cc \u06cc\u06a9 \u0633\u0627\u0645\u0627\u0646\u0647 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645\u06cc\u060c \u0628\u0627 \u0639\u0646\u0635\u0631\u0647\u0627\u06cc \u0641\u0636\u0627\u06cc \u0647\u06cc\u0644\u0628\u0631\u062a \u0646\u0645\u0627\u06cc\u0634 \u0645\u06cc \u062f\u0647\u06cc\u0645. \u0627\u06cc\u0646 \u0639\u0646\u0627\u0635\u0631\u060c \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc \u062d\u0627\u0644\u062a \u0646\u0627\u0645\u06cc\u062f\u0647 \u0645\u06cc \u0634\u0648\u0646\u062f. \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc \u062d\u0627\u0644\u062a \u062f\u0631 \u067e\u0627\u06cc\u0647 \u0647\u0627\u06cc \u0645\u062a\u0641\u0627\u0648\u062a \u0628\u0648\u0633\u06cc\u0644\u0647 \u0628\u0633\u0637 \u062a\u0627\u0628\u0639 \u0647\u0627 \u0646\u0645\u0627\u06cc\u0634 \u067e\u0630\u06cc\u0631\u0646\u062f. \u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc \u0641\u0636\u0627\u06cc \u062f\u06a9\u0627\u0631\u062a\u06cc \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u062f\u0631 \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u062e\u062a\u0635\u0627\u062a \u0647\u0627\u06cc \u06af\u0648\u0646\u0627\u06af\u0648\u0646 (\u0645\u062b\u0644\u0627 \u0628\u0627 \u0627\u0646\u062f\u06a9\u06cc \u062f\u0648\u0631\u0627\u0646 \u0646\u0633\u0628\u062a \u0628\u0647 \u06cc\u06a9\u062f\u06cc\u06af\u0631) \u0646\u0645\u0627\u06cc\u0634 \u062f\u0627\u062f. \u0642\u0637\u0639\u0627 \u0628\u0631\u062f\u0627\u0631 \u0645\u0648\u062c\u0648\u062f \u062f\u0631 \u0641\u0636\u0627\u06cc \u062f\u06a9\u0627\u0631\u062a\u06cc \u0645\u0633\u062a\u0642\u0644 \u0627\u0632 \u067e\u0627\u06cc\u0647 \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u062e\u062a\u0635\u0627\u062a\u06cc \u0627\u0633\u062a \u06a9\u0647 \u062f\u0631 \u0622\u0646 \u0628\u0633\u0637 \u062f\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f. \u0627\u06cc\u0646 \u0642\u0636\u06cc\u0647 \u0628\u0631\u0627\u06cc \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc \u062d\u0627\u0644\u062a \u0633\u0627\u0645\u0627\u0646\u0647 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645\u06cc \u0646\u06cc\u0632 \u0635\u0627\u062f\u0642 \u0627\u0633\u062a. \u0628\u0631\u0627\u06cc \u0627\u0633\u062a\u0642\u0644\u0627\u0644 \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc \u062d\u0627\u0644\u062a \u0627\u0632 \u0645\u062e\u062a\u0635\u0627\u062a\u060c \u067e\u0644 \u062f\u06cc\u0631\u0627\u06a9 \u0646\u0645\u0627\u062f\u06af\u0630\u0627\u0631\u06cc \u0627\u0631\u0632\u0634\u0645\u0646\u062f \u062e\u0648\u062f \u0631\u0627 \u062a\u0628\u06cc\u06cc\u0646 \u06a9\u0631\u062f.<\/p>\n<h3>1-4 \u06a9\u062a<\/h3>\n<p>\u062f\u06cc\u0631\u0627\u06a9 \u0628\u0631\u062f\u0627\u0631 \u062d\u0627\u0644\u062a $\\psi$ \u0631\u0627 \u0628\u0627 \u0646\u0645\u0627\u062f $| \\psi \\rangle$ \u0646\u0645\u0627\u06cc\u0634 \u062f\u0627\u062f \u06a9\u0647 \u0628\u0631\u062f\u0627\u0631 \u06a9\u062a (Ket) \u06cc\u0627 \u0628\u0647 \u0633\u0627\u062f\u06af\u06cc \u06a9\u062a \u0646\u0627\u0645\u06cc\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f. \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc \u06a9\u062a \u0631\u0627 \u0628\u0627 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0647\u0627\u06cc \u0633\u062a\u0648\u0646\u06cc \u0646\u0645\u0627\u06cc\u0634 \u0645\u06cc \u062f\u0647\u06cc\u0645. \u06a9\u062a \u0647\u0627 \u0628\u0647 \u0641\u0636\u0627\u06cc \u0647\u06cc\u0644\u0628\u0631\u062a $\\mathcal{H}$ \u06cc\u0627 \u0641\u0636\u0627\u06cc \u06a9\u062a \u062a\u0639\u0644\u0642 \u062f\u0627\u0631\u0646\u062f.<\/p>\n<h3>2-4 \u0628\u0631\u0627<\/h3>\n<p>\u0628\u0647 \u0627\u0632\u0627\u06cc \u0647\u0631 \u06a9\u062a\u060c \u06cc\u06a9 \u0628\u0631\u062f\u0627\u0631 \u0628\u0631\u0627 \u06cc\u0627 \u0628\u0647 \u0633\u0627\u062f\u06af\u06cc (Bra) \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06a9\u0647 \u0628\u0647 \u0641\u0636\u0627\u06cc \u0647\u0645\u0632\u0627\u062f $\\mathcal{H}_d$ \u0645\u062a\u0639\u0644\u0642 \u0627\u0633\u062a \u0648 \u0628\u0627 $\\langle \\psi |$ \u0646\u0645\u0627\u06cc\u0634 \u0645\u06cc \u062f\u0647\u06cc\u0645. \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc \u0628\u0631\u0627 \u0631\u0627 \u0628\u0627 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0647\u0627\u06cc \u0633\u0637\u0631\u06cc \u0646\u0645\u0627\u06cc\u0634 \u0645\u06cc \u062f\u0647\u06cc\u0645. \u0628\u0631\u062f\u0627\u0631 \u0628\u0631\u0627\u060c \u062a\u0631\u0627\u0646\u0647\u0627\u062f\u0647 \u0645\u062e\u062a\u0644\u0637 \u0628\u0631\u062f\u0627\u0631 \u06a9\u062a \u0627\u0633\u062a. \u0628\u0631\u0627\u06cc \u0645\u062b\u0627\u0644 \u0627\u06af\u0631 $a$ \u0648 $b$ \u062f\u0648 \u0639\u062f\u062f \u0645\u062e\u062a\u0644\u0637 \u0648 \u062f\u0631\u0627\u06cc\u0647 \u0647\u0627\u06cc \u06a9\u062a \u0628\u0627\u0634\u0646\u062f\u060c \u0631\u0627\u0628\u0637\u0647 \u06a9\u062a \u0648 \u0628\u0631\u0627 \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u0627\u0633\u062a:<\/p>\n<p><strong>(1)<\/strong><\/p>\n<p dir=\"ltr\" style=\"text-align: center;\">$\\large | \\psi \\rangle = \\begin{bmatrix} a \\\\ b \\end{bmatrix} \\leftrightarrow \\langle \\psi |= \\begin{bmatrix} a^* &amp; b^* \\end{bmatrix}$<\/p>\n<h3>3-4 \u0628\u0631\u0627-\u06a9\u062a<\/h3>\n<p>\u0646\u0645\u0627\u062f\u06af\u0630\u0627\u0631\u06cc \u0636\u0631\u0628 \u062f\u0627\u062e\u0644\u06cc \u0646\u06cc\u0632 \u0628\u0627 \u0628\u0631\u0627-\u06a9\u062a \u0642\u0627\u0628\u0644 \u062a\u0648\u0635\u06cc\u0641 \u0627\u0633\u062a. \u0627\u06cc\u0646 \u0636\u0631\u0628 \u062f\u0627\u062e\u0644\u06cc \u0628\u0647 \u0635\u0648\u0631\u062a $\\langle \\phi | \\psi \\rangle$ \u0646\u0645\u0627\u06cc\u0634 \u062f\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f \u06a9\u0647 \u0628\u0631\u0627\u06cc \u0633\u0647\u0648\u0644\u062a \u0646\u0645\u0627\u06cc\u0634\u060c \u062a\u0646\u0647\u0627 \u06cc\u06a9\u06cc \u0627\u0632 \u062e\u0637\u0648\u0637 \u0639\u0645\u0648\u062f\u06cc \u0628\u0631\u0627 \u0648 \u06a9\u062a \u0631\u0627 \u0645\u06cc \u0646\u0648\u06cc\u0633\u06cc\u0645. \u0627\u0632 \u062f\u06cc\u062f\u06af\u0627\u0647 \u0645\u0627\u062a\u0631\u06cc\u0633\u06cc \u0646\u06cc\u0632 \u0636\u0631\u0628 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0633\u0637\u0631\u06cc \u062f\u0631 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0633\u062a\u0648\u0646\u06cc \u0647\u0645\u0648\u0627\u0631\u0647 \u06cc\u06a9 \u0639\u062f\u062f \u0627\u0633\u062a\u061b \u0628\u0647 \u0647\u0645\u06cc\u0646 \u062f\u0644\u06cc\u0644 \u0646\u0648\u0634\u062a\u0646 \u0628\u0635\u0648\u0631\u062a \u0628\u0631\u0627-\u06a9\u062a \u0627\u0647\u0645\u06cc\u062a \u062f\u0627\u0631\u062f. \u0636\u0631\u0628 \u0639\u062f\u062f \u0645\u062e\u062a\u0644\u0637 \u062f\u0631 \u06a9\u062a(\u0628\u0631\u0627) \u06cc\u06a9 \u06a9\u062a(\u0628\u0631\u0627) \u0628\u062f\u0633\u062a \u0645\u06cc \u062f\u0647\u062f \u0648 \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0648\u0631\u062f \u0628\u0627 \u0628\u0631\u062f\u0627\u0631\u0647\u0627 \u062a\u0641\u0627\u0648\u062a\u06cc \u0646\u062f\u0627\u0631\u062f.<\/p>\n<h3>4-4 \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u0646\u0645\u0627\u062f\u06af\u0630\u0627\u0631\u06cc \u062f\u06cc\u0631\u0627\u06a9<\/h3>\n<p>\u0646\u0645\u0627\u062f\u06af\u0630\u0627\u0631\u06cc \u062f\u06cc\u0631\u0627\u06a9 \u062e\u0635\u0648\u0635\u06cc\u0627\u062a\u06cc \u062f\u0627\u0631\u062f \u06a9\u0647 \u0622\u0646 \u0647\u0627 \u0631\u0627 \u062f\u0631 \u0627\u06cc\u0646 \u0628\u062e\u0634 \u0630\u06a9\u0631 \u0645\u06cc \u06a9\u0646\u0645:<\/p>\n<ul>\n<li>\n<h6><strong>\u0628\u0647 \u0627\u0632\u0627\u06cc \u0647\u0631 \u06a9\u062a\u060c \u06cc\u06a9 \u0628\u0631\u0627 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f<\/strong><\/h6>\n<\/li>\n<\/ul>\n<p>\u0628\u0647 \u0627\u0632\u0627\u06cc \u0647\u0631 \u06a9\u062a\u060c \u0628\u0631\u0627 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u0648 \u0628\u0631\u0639\u06a9\u0633 : $|\\psi \\rangle \\leftrightarrow \\langle \\psi |$<\/p>\n<p>\u0645\u06cc \u062a\u0648\u0627\u0646 \u0647\u0631 \u0636\u0631\u06cc\u0628 \u0645\u062e\u062a\u0644\u0637 \u0631\u0627 \u0627\u0632 \u06a9\u062a \u062e\u0627\u0631\u062c \u06a9\u0631\u062f \u0627\u0645\u0627 \u0628\u0631\u0627\u06cc \u062e\u0631\u0648\u062c \u0636\u0631\u06cc\u0628 \u0645\u062e\u062a\u0644\u0637 \u0627\u0632 \u0628\u0631\u0627\u060c \u0628\u0627\u06cc\u062f \u0645\u0632\u062f\u0648\u062c \u0622\u0646 \u0631\u0627 \u062c\u0644\u0648\u06cc \u0628\u0631\u0627 \u0646\u0648\u0634\u062a\u060c $a$ \u06cc\u06a9 \u0639\u062f\u062f \u0645\u062e\u062a\u0644\u0637 \u0627\u0633\u062a:<\/p>\n<p dir=\"ltr\" style=\"text-align: center;\">$|a\\psi \\rangle=a|\\psi \\rangle \\; , \\; \\langle a \\psi |=a^*\\langle \\psi |$<\/p>\n<p>\u0645\u06cc\u0627\u0646 \u0628\u0631\u0627\u0647\u0627 \u0648 \u06a9\u062a \u0647\u0627 \u062a\u0646\u0627\u0638\u0631\u06cc \u06cc\u06a9 \u0628\u0647 \u06cc\u06a9 \u0645\u0648\u062c\u0648\u062f \u0627\u0633\u062a\u061b $a$ \u0648 $b$ \u062f\u0648 \u0639\u062f\u062f \u0645\u062e\u062a\u0644\u0637 \u0627\u0646\u062f.:<\/p>\n<p dir=\"ltr\" style=\"text-align: center;\">$a|\\psi \\rangle + b|\\phi \\rangle \\leftrightarrow a^*\\langle \\psi |+b^*\\langle \\phi |$<\/p>\n<ul>\n<li>\n<h6><strong>\u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u0636\u0631\u0628 \u062f\u0627\u062e\u0644\u06cc<\/strong><\/h6>\n<\/li>\n<\/ul>\n<p>\u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u067e\u06cc\u0634\u062a\u0631 \u06af\u0641\u062a\u0645\u061b \u062a\u0631\u062a\u06cc\u0628 \u062f\u0631 \u0636\u0631\u0628 \u062f\u0627\u062e\u0644\u06cc \u0645\u06a9\u0627\u0646\u06cc\u06a9 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645\u06cc \u062f\u0627\u0631\u0627\u06cc \u0627\u0647\u0645\u06cc\u062a \u0627\u0633\u062a. \u062c\u0627\u0628\u062c\u0627 \u06a9\u0631\u062f\u0646 \u0628\u0631\u0627 \u0648 \u06a9\u062a \u062f\u0631 \u0636\u0631\u0628 \u0646\u0631\u062f\u0647 \u0627\u06cc\u060c \u0628\u0647 \u0627\u0646\u062f\u0627\u0632\u0647 \u0645\u0632\u062f\u0648\u062c \u0645\u062e\u062a\u0644\u0637 \u06af\u0631\u0641\u062a\u0646 \u0627\u0632 \u062d\u0627\u0635\u0644 \u0647\u0632\u06cc\u0646\u0647 \u062f\u0627\u0631\u062f:<\/p>\n<p dir=\"ltr\" style=\"text-align: center;\">$\\langle \\phi |\\psi \\rangle^* = \\langle \\psi |\\phi \\rangle$<\/p>\n<p>\u0637\u0628\u06cc\u0639\u062a\u0627 \u0627\u06af\u0631 \u062f\u0648 \u0628\u0631\u062f\u0627\u0631 \u062d\u0627\u0644\u062a \u062d\u0642\u06cc\u0642\u06cc \u0628\u0627\u0634\u0646\u062f\u060c \u0636\u0631\u0628 \u062f\u0627\u062e\u0644\u06cc \u062c\u0627\u0628\u062c\u0627\u06cc\u06cc \u067e\u0630\u06cc\u0631 \u0627\u0633\u062a. \u062f\u06cc\u062f\u0646 \u0641\u0647\u0631\u0633\u062a \u0686\u0646\u062f \u0648\u06cc\u0698\u06af\u06cc \u062f\u06cc\u06af\u0631 \u0636\u0631\u0628 \u062f\u0627\u062e\u0644\u06cc \u062e\u0627\u0644\u06cc \u0627\u0632 \u0644\u0637\u0641 \u0646\u06cc\u0633\u062a (\u0627\u06cc\u0646 \u0647\u0627 \u0627\u0632 \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u0642\u0628\u0644\u06cc \u0648 \u062e\u0637\u06cc \u0628\u0648\u062f\u0646 \u0636\u0631\u0628 \u062f\u0627\u062e\u0644\u06cc \u0646\u0634\u0627\u062a \u0645\u06cc \u06af\u06cc\u0631\u0646\u062f):<\/p>\n<p><strong>(2)<\/strong><\/p>\n<p dir=\"ltr\" style=\"text-align: center;\">$\\langle \\phi |a\\psi_1+b\\psi_2 \\rangle=a\\langle \\phi |\\psi_1 \\rangle+b\\langle \\phi |\\psi_2 \\rangle$<\/p>\n<p><strong>(3)<\/strong><\/p>\n<p dir=\"ltr\" style=\"text-align: center;\">$\\langle c\\phi_1+d\\phi_2 |\\psi \\rangle=c^*\\langle \\phi_1 |\\psi \\rangle+d^*\\langle \\phi_2 |\\psi \\rangle$<\/p>\n<p><strong>(4)<\/strong><\/p>\n<p dir=\"ltr\" style=\"text-align: center;\">$\\small \\langle c\\phi_1+d\\phi_2 |a\\psi_1+b\\psi_2 \\rangle=c^*a\\langle \\phi_1 |\\psi_1 \\rangle+c^*b\\langle \\phi_1 |\\psi_2 \\rangle + d^*a\\langle \\phi_2 |\\psi_1 \\rangle+d^*b\\langle \\phi_2 |\\psi_2 \\rangle$<\/p>\n<ul>\n<li>\n<h6><strong>\u0646\u0631\u0645 \u0647\u0645\u0648\u0627\u0631\u0647 \u062d\u0642\u06cc\u0642\u06cc \u0648 \u0646\u0627\u0645\u0646\u0641\u06cc \u0627\u0633\u062a.<\/strong><\/h6>\n<\/li>\n<\/ul>\n<p>\u0628\u0647 \u0627\u0632\u0627\u06cc \u0647\u0631 \u0628\u0631\u062f\u0627\u0631 \u062d\u0627\u0644\u062a $|\\psi \\rangle$ \u0641\u0636\u0627\u06cc \u0647\u06cc\u0644\u0628\u0631\u062a $\\mathcal{H}$\u060c \u0646\u0631\u0645 \u0628\u0631\u062f\u0627\u0631 \u06cc\u0627 $\\langle \\psi |\\psi \\rangle$ \u0647\u0645\u0648\u0627\u0631\u0647 \u0645\u062b\u0628\u062a \u0627\u0633\u062a. \u062a\u0646\u0647\u0627 \u062f\u0631 \u0635\u0648\u0631\u062a\u06cc \u06a9\u0647 \u0628\u0631\u062f\u0627\u0631 \u062d\u0627\u0644\u062a\u060c \u0628\u0631\u062f\u0627\u0631 \u0635\u0641\u0631 \u0628\u0627\u0634\u062f\u061b \u0646\u0631\u0645 \u0635\u0641\u0631 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f. \u062f\u0631 \u0635\u0648\u0631\u062a\u06cc \u06a9\u0647 \u0628\u0631\u062f\u0627\u0631 \u0628\u0647\u0646\u062c\u0627\u0631 \u0628\u0627\u0634\u062f \u0646\u0631\u0645 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u06cc\u06a9 \u0627\u0633\u062a ($\\langle \\psi |\\psi \\rangle=1$).<\/p>\n<ul>\n<li>\n<h6><strong>\u0646\u0627\u0645\u0633\u0627\u0648\u06cc \u0634\u0648\u0627\u0631\u062a\u0632<\/strong><\/h6>\n<\/li>\n<\/ul>\n<p>\u0628\u0631\u0627\u06cc \u062f\u0648 \u0628\u0631\u062f\u0627\u0631 \u062d\u0627\u0644\u062a \u062f\u0644\u062e\u0648\u0627\u0647 $|\\psi \\rangle$ \u0648 $|\\phi \\rangle$ \u062f\u0631 \u0641\u0636\u0627\u06cc \u0647\u06cc\u0644\u0628\u0631\u062a\u060c \u0646\u0627\u0645\u0633\u0627\u0648\u06cc \u0634\u0648\u0627\u0631\u062a\u0632 \u0628\u0631\u0642\u0631\u0627\u0631 \u0627\u0633\u062a (\u0627\u062b\u0628\u0627\u062a \u062f\u0631 <a href=\"http:\/\/localhost\/saturnscience.com\/62-%d9%81%d8%b6%d8%a7%db%8c-%d9%87%db%8c%d9%84%d8%a8%d8%b1%d8%aa\/\">\u0645\u062b\u0627\u0644 62-1<\/a>):<\/p>\n<p><strong>(5)<\/strong><\/p>\n<p dir=\"ltr\" style=\"text-align: center;\">$\\large |\\langle \\psi | \\phi\\rangle |^2 \\leq \\langle \\psi | \\psi \\rangle \\langle \\phi | \\phi \\rangle$<\/p>\n<p>\u0627\u06af\u0631 $|\\psi \\rangle$ \u0648 $|\\phi \\rangle$ \u0648\u0627\u0628\u0633\u062a\u0647 \u062e\u0637\u06cc \u06cc\u06a9\u062f\u06cc\u06af\u0631 \u0628\u0627\u0634\u0646\u062f (\u06cc\u06a9\u06cc \u0636\u0631\u06cc\u0628 \u0627\u0632 \u062f\u06cc\u06af\u0631\u06cc \u0628\u0627\u0634\u062f \u0645\u062b\u0644\u0627 $|\\psi \\rangle =a |\\phi \\rangle$ \u06a9\u0647 $a$ \u0627\u0633\u06a9\u0627\u0644\u0631 \u0627\u0633\u062a). \u062a\u0633\u0627\u0648\u06cc \u0628\u0631\u0642\u0631\u0627\u0631 \u0645\u06cc \u0634\u0648\u062f (\u062a\u0645\u0631\u06cc\u0646 65-1). \u0645\u0634\u0627\u0628\u0647 \u0627\u06cc\u0646 \u0631\u0627\u0628\u0637\u0647 \u0631\u0627 \u062f\u0631 \u0641\u0636\u0627\u06cc \u0627\u0642\u0644\u06cc\u062f\u0633\u06cc \u0646\u06cc\u0632 \u062f\u0627\u0631\u06cc\u0645:<\/p>\n<p><strong>(6)<\/strong><\/p>\n<p dir=\"ltr\" style=\"text-align: center;\">$\\large |\\vec{a}.\\vec{b}|^2 \\leq |\\vec{a}|^2 |\\vec{b}|^2$<\/p>\n<ul>\n<li>\n<h6><strong>\u0646\u0627\u0645\u0633\u0627\u0648\u06cc \u0645\u062b\u0644\u062b<\/strong><\/h6>\n<\/li>\n<\/ul>\n<p><strong>(7)<\/strong><\/p>\n<p dir=\"ltr\" style=\"text-align: center;\">$\\large \\sqrt{\\langle \\psi+\\phi | \\psi+\\phi \\rangle} \\leq \\sqrt{\\langle \\psi | \\psi\\rangle} + \\sqrt{\\langle \\phi | \\phi\\rangle}$<\/p>\n<p>\u062f\u0631 \u0635\u0648\u0631\u062a\u06cc \u06a9\u0647 $|\\psi \\rangle$ \u0648 $|\\phi \\rangle$ \u0648\u0627\u0628\u0633\u062a\u0647 \u062e\u0637\u06cc \u06cc\u06a9\u062f\u06cc\u06af\u0631 \u0628\u0627\u0634\u0646\u062f\u061b \u0631\u0627\u0628\u0637\u0647 \u0628\u0627\u0644\u0627 \u062a\u0633\u0627\u0648\u06cc \u0645\u06cc \u0634\u0648\u062f. \u0647\u0645\u0627\u0646\u0646\u062f \u0627\u06cc\u0646 \u0646\u0627\u0645\u0633\u0627\u0648\u06cc \u0631\u0627 \u062f\u0631 \u0641\u0636\u0627\u06cc \u0627\u0642\u0644\u06cc\u062f\u0633\u06cc \u0646\u06cc\u0632 \u062f\u0627\u0631\u06cc\u0645:<\/p>\n<p><strong>(8)<\/strong><\/p>\n<p dir=\"ltr\" style=\"text-align: center;\">$\\large |\\vec{a}+\\vec{b}| \\leq |\\vec{a}|+|\\vec{b}|$<\/p>\n<ul>\n<li>\n<h6>\u062d\u0627\u0644\u062a \u0647\u0627\u06cc \u0645\u062a\u0639\u0627\u0645\u062f<\/h6>\n<\/li>\n<\/ul>\n<p>\u0647\u0631\u06af\u0627\u0647 \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u062f\u0627\u062e\u0644\u06cc \u062f\u0648 \u0628\u0631\u062f\u0627\u0631 \u062d\u0627\u0644\u062a $|\\psi \\rangle$ \u0648 $|\\phi \\rangle$ \u0635\u0641\u0631 \u0628\u0627\u0634\u062f\u060c \u0622\u0646\u06af\u0627\u0647 \u062f\u0648 \u0628\u0631\u062f\u0627\u0631 \u0645\u062a\u0639\u0627\u0645\u062f\u0646\u062f:<\/p>\n<p><strong>(9)<\/strong><\/p>\n<p dir=\"ltr\" style=\"text-align: center;\">$\\large \\langle \\psi | \\phi\\rangle = 0$<\/p>\n<ul>\n<li>\n<h6>\u062d\u0627\u0644\u062a \u0647\u0627\u06cc \u0645\u062a\u0639\u0627\u0645\u062f \u0628\u0647\u0646\u062c\u0627\u0631<\/h6>\n<\/li>\n<\/ul>\n<p>\u062f\u0648 \u0628\u0631\u062f\u0627\u0631 \u062d\u0627\u0644\u062a \u06a9\u0647 \u0646\u0631\u0645 \u0622\u0646 \u0647\u0627 \u06cc\u06a9 \u0627\u0633\u062a \u0648 \u0628\u0627 \u0647\u0645 \u0645\u062a\u0639\u0627\u0645\u062f\u0646\u062f\u061b \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc \u0645\u062a\u0639\u0627\u0645\u062f \u0628\u0647\u0646\u062c\u0627\u0631\u0646\u062f:<\/p>\n<p><strong>(10)<\/strong><\/p>\n<p dir=\"ltr\" style=\"text-align: center;\">$\\large \\langle \\psi | \\phi\\rangle = 0 \\; , \\;\u00a0\\langle \\psi | \\psi\\rangle = 1 \\; , \\; \\langle \\phi | \\phi\\rangle = 1$<\/p>\n<ul>\n<li>\n<h6>\u06a9\u0645\u06cc\u062a \u0647\u0627\u06cc \u0645\u0645\u0646\u0648\u0639\u0647<\/h6>\n<\/li>\n<\/ul>\n<p>\u0627\u06af\u0631 \u062f\u0648 \u0628\u0631\u062f\u0627\u0631 \u062d\u0627\u0644\u062a $|\\psi \\rangle$ \u0648 $|\\phi \\rangle$\u060c \u0645\u062a\u0639\u0644\u0642 \u0628\u0647 \u06cc\u06a9 \u0641\u0636\u0627\u06cc \u0628\u0631\u062f\u0627\u0631\u06cc (\u0647\u06cc\u0644\u0628\u0631\u062a) \u0628\u0627\u0634\u0646\u062f. \u0636\u0631\u0628 \u0647\u0627\u06cc \u06a9\u062a-\u06a9\u062a\u00a0 $|\\psi \\rangle |\\phi \\rangle$ \u0648 \u0628\u0631\u0627-\u0628\u0631\u0627 $\\langle \\psi |\\langle \\phi |$ \u0645\u0645\u0646\u0648\u0639 \u0648 \u0628\u06cc \u0645\u0639\u0646\u06cc \u0627\u0646\u062f. \u0627\u0632 \u062f\u06cc\u062f\u06af\u0627\u0647 \u0645\u0627\u062a\u0631\u06cc\u0633\u06cc \u0646\u06cc\u0632 \u0648\u0627\u0636\u062d \u0627\u0633\u062a \u06a9\u0647 \u0636\u0631\u0628 \u0645\u0627\u062a\u0631\u06cc\u0633\u06cc \u062f\u0648 \u0628\u0631\u062f\u0627\u0631 \u0633\u062a\u0648\u0646\u06cc \u06cc\u0627 \u062f\u0648 \u0628\u0631\u062f\u0627\u0631 \u0633\u0637\u0631\u06cc \u0627\u0645\u06a9\u0627\u0646 \u067e\u0630\u06cc\u0631 \u0646\u06cc\u0633\u062a. \u0627\u06af\u0631 $|\\psi \\rangle$ \u0648 $|\\phi \\rangle$\u060c \u0628\u0647 \u062f\u0648 \u0641\u0636\u0627\u06cc \u0628\u0631\u062f\u0627\u0631\u06cc \u0645\u062a\u0641\u0627\u0648\u062a \u062a\u0639\u0644\u0642 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u0646\u062f. \u062a\u0646\u0647\u0627 \u0636\u0631\u0628 \u062a\u0627\u0646\u0633\u0648\u0631\u06cc \u062f\u0648 \u0628\u0631\u062f\u0627\u0631\u062d\u0627\u0644\u062a $|\\psi \\rangle \\otimes |\\phi \\rangle$ \u0645\u0639\u0646\u06cc \u062f\u0627\u0631 \u0648 \u0642\u0627\u0628\u0644 \u0627\u0646\u062c\u0627\u0645 \u0627\u0633\u062a.<\/p>\n<h5>* \u0645\u062b\u0627\u0644 4-1)<\/h5>\n<p>\u062f\u0648 \u0628\u0631\u062f\u0627\u0631 \u062d\u0627\u0644\u062a $|\\psi \\rangle =3i |\\phi_1 \\rangle -7i |\\phi_2 \\rangle $ \u0648 $| \\chi \\rangle =-|\\phi_1 \\rangle +2i |\\phi_2 \\rangle $ \u06a9\u0647 \u062f\u0631 \u0622\u0646\u0647\u0627 \u062f\u0648 \u0628\u0631\u062f\u0627\u0631 $|\\phi_1 \\rangle$ \u0648 $|\\phi_2 \\rangle$ \u0645\u062a\u0639\u0627\u0645\u062f \u0628\u0647\u0646\u062c\u0627\u0631\u0646\u062f.<\/p>\n<p>\u0627\u0644\u0641) $| \\psi+\\chi \\rangle$ \u0648 $\\langle \\psi+\\chi |$ \u0631\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u06a9\u0646\u06cc\u062f<\/p>\n<p>\u0628) \u0636\u0631\u0628 \u0647\u0627\u06cc \u062f\u0627\u062e\u0644\u06cc $\\langle \\psi | \\chi \\rangle$ \u0648 $\\langle \\chi | \\psi \\rangle$ \u0631\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u06a9\u0646\u06cc\u062f\u061b \u0622\u06cc\u0627 \u062f\u0648 \u06a9\u0645\u06cc\u062a \u06cc\u06a9\u0633\u0627\u0646\u0646\u062f\u061f<\/p>\n<h5>\u067e\u0627\u0633\u062e<\/h5>\n<p><strong>\u0627\u0644\u0641)<\/strong><\/p>\n<p>\u06a9\u0627\u0641\u06cc \u0627\u0633\u062a \u0645\u0648\u0644\u0641\u0647 \u0628\u0647 \u0645\u0648\u0644\u0641\u0647 \u062c\u0645\u0639 \u06a9\u062a \u0647\u0627 \u0635\u0648\u0631\u062a \u06af\u06cc\u0631\u062f \u062a\u0627 $| \\psi+\\chi \\rangle$ \u0645\u062d\u0627\u0633\u0628\u0647 \u0634\u0648\u062f:<\/p>\n<p dir=\"ltr\">$| \\psi+\\chi \\rangle=(3i-1)|\\phi_1 \\rangle+(-5i)|\\phi_2 \\rangle $<\/p>\n<p>\u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 $\\langle \\psi+\\chi |$\u060c \u06a9\u0627\u0641\u06cc \u0627\u0633\u062a \u0627\u0632 \u0636\u0631\u0627\u06cc\u0628 \u0628\u0627\u0644\u0627 \u0645\u0632\u062f\u0648\u062c \u0645\u062e\u062a\u0644\u0637 \u0628\u06af\u06cc\u0631\u06cc\u0645 \u0648 \u0622\u0646\u0647\u0627 \u0631\u0627 \u062f\u0631 \u0628\u0631\u0627\u0628\u0631 \u0628\u0631\u0627\u0647\u0627\u06cc \u0645\u062a\u0646\u0627\u0638\u0631 $\\phi_i$ \u0645\u06cc \u0646\u0648\u06cc\u0633\u06cc\u0645:<\/p>\n<p dir=\"ltr\">$\\langle \\psi+\\chi |=(-3i-1)\\langle \\phi_1 | + (5i) \\langle \\phi_2 |$<\/p>\n<p><strong>\u0628)\u00a0<\/strong>\u0686\u0648\u0646 \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc \u067e\u0627\u06cc\u0647 \u0645\u062a\u0639\u0627\u0645\u062f \u0628\u0647\u0646\u062c\u0627\u0631\u0646\u062f\u061b \u062a\u0646\u0647\u0627 \u06a9\u0627\u0641\u06cc \u0627\u0633\u062a \u0628\u0631\u062f\u0627\u0631 \u0628\u0631\u0627\u06cc $\\psi$ \u0631\u0627 \u062d\u0633\u0627\u0628 \u06a9\u0646\u06cc\u0645 \u0648 \u0645\u0648\u0644\u0641\u0647 \u0647\u0627\u06cc \u0622\u0646 \u0631\u0627 \u062f\u0631 \u0645\u0648\u0644\u0641\u0647 \u0647\u0627\u06cc \u06a9\u062a $\\chi$ \u0636\u0631\u0628 \u06a9\u0646\u06cc\u0645 \u0648 \u062f\u0631 \u0622\u062e\u0631 \u062c\u0645\u0639 \u06a9\u0646\u06cc\u0645 \u062a\u0627 $\\langle \\psi | \\chi \\rangle$ \u062d\u0633\u0627\u0628 \u0634\u0648\u062f:<\/p>\n<p dir=\"ltr\">$\\langle \\psi | \\chi \\rangle=(-3i,7i).(-1,2i)=3i-14$<\/p>\n<p>\u0645\u0634\u0627\u0628\u0647 \u06a9\u0627\u0631 \u0628\u0627\u0644\u0627 \u0631\u0627 \u0628\u0631\u0627\u06cc $\\langle \\chi | \\psi \\rangle$ \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc \u062f\u0647\u06cc\u0645:<\/p>\n<p dir=\"ltr\">$\\langle \\chi | \\psi \\rangle=(-1,-2i).(3i,-7i)=-3i-14$<\/p>\n<p>\u06a9\u0645\u06cc\u062a \u0647\u0627\u06cc \u0645\u062d\u0627\u0633\u0628\u0647 \u0634\u062f\u0647 \u0628\u0631\u0627\u0628\u0631 \u0646\u06cc\u0633\u062a\u0646\u062f \u0648 \u0645\u0632\u062f\u0648\u062c \u0645\u062e\u062a\u0644\u0637 \u06cc\u06a9\u062f\u06cc\u06af\u0631\u0646\u062f \u06a9\u0647 \u0627\u0646\u062a\u0638\u0627\u0631\u0634 \u0631\u0627 \u062f\u0627\u0634\u062a\u06cc\u0645.<\/p>\n<hr \/>\n<h3 style=\"text-align: right;\">5-4 \u0645\u0641\u0647\u0648\u0645 \u0641\u06cc\u0632\u06cc\u06a9\u06cc \u0636\u0631\u0628 \u062f\u0627\u062e\u0644\u06cc<\/h3>\n<p>\u0636\u0631\u0628 \u062f\u0627\u062e\u0644\u06cc \u0645\u06a9\u0627\u0646\u06cc\u06a9 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645\u06cc \u0628\u0647 \u062f\u0648 \u0631\u0648\u0634 \u062a\u0641\u0633\u06cc\u0631 \u0645\u06cc \u0634\u0648\u062f. \u0631\u0648\u0634 \u0646\u062e\u0633\u062a \u0627\u06cc\u0646\u06a9\u0647 \u0647\u0645\u0627\u0646\u0646\u062f \u0641\u0636\u0627\u06cc \u0627\u0642\u0644\u06cc\u062f\u0633\u06cc &#8211; \u06a9\u0647 \u062f\u0631 \u0622\u0646 $\\vec{a}.\\vec{b}$ \u062a\u0635\u0648\u06cc\u0631 \u0628\u0631\u062f\u0627\u0631 $\\vec{b}$ \u0628\u0631 \u0628\u0631\u062f\u0627\u0631 $\\vec{a}$ \u0631\u0627 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u062f &#8211; \u0636\u0631\u0628 $\\langle \\phi | \\psi \\rangle$ \u062a\u0635\u0648\u06cc\u0631 $|\\psi \\rangle$ \u0628\u0631 $|\\phi \\rangle$ \u0627\u0633\u062a. \u0631\u0648\u0634 \u062f\u06cc\u06af\u0631 \u0628\u0631\u0627\u06cc \u062d\u0627\u0644\u062a \u0647\u0627\u06cc \u0628\u0647\u0646\u062c\u0627\u0631\u060c \u0628\u0627 \u062a\u0639\u0628\u06cc\u0631 \u0622\u0645\u0627\u0631\u06cc \u0628\u0648\u0631\u0646 \u0645\u0637\u0627\u0628\u0642\u062a \u062f\u0627\u0631\u062f. \u06a9\u0645\u06cc\u062a $\\langle \\phi | \\psi \\rangle$ \u062f\u0627\u0645\u0646\u0647 \u0627\u062d\u062a\u0645\u0627\u0644\u06cc \u06a9\u0647 \u062d\u0627\u0644\u062a \u0633\u0627\u0645\u0627\u0646\u0647 $|\\psi \\rangle$ \u067e\u0633 \u0627\u0632 \u0627\u0646\u062c\u0627\u0645 \u06cc\u06a9 \u0627\u0646\u062f\u0627\u0632\u0647 \u06af\u06cc\u0631\u06cc \u0628\u0631 \u0633\u0627\u0645\u0627\u0646\u0647\u060c \u062f\u0631 \u062d\u0627\u0644\u062a \u062f\u06cc\u06af\u0631 $|\\phi \\rangle$ \u0628\u0627\u0634\u062f \u0631\u0627 \u0646\u0645\u0627\u06cc\u0634 \u0645\u06cc \u062f\u0647\u062f.<\/p>\n<h3>6-4 \u062c\u0645\u0639 \u0628\u0646\u062f\u06cc \u0641\u0635\u0644<\/h3>\n<p>\u0628\u0627 \u0646\u0645\u0627\u062f\u06af\u0630\u0627\u0631\u06cc \u062f\u06cc\u0631\u0627\u06a9 \u0648 \u062e\u0635\u0648\u0635\u06cc\u0627\u062a \u0628\u0631\u0627\u060c \u06a9\u062a \u0648 \u0628\u0631\u0627-\u06a9\u062a \u0622\u0634\u0646\u0627 \u0634\u062f\u06cc\u0645. \u0647\u0645\u0686\u0646\u06cc\u0646 \u0645\u0641\u0647\u0648\u0645 \u0641\u06cc\u0632\u06cc\u06a9\u06cc \u0636\u0631\u0628 \u062f\u0627\u062e\u0644\u06cc \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u0646\u0645\u0648\u062f\u06cc\u0645.<\/p>\n<p style=\"text-align: center;\">\n<p>&nbsp;<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 48px;\">\n<tbody>\n<tr style=\"height: 48px;\">\n<td style=\"width: 100%; text-align: center; height: 48px;\"><span style=\"font-size: 24pt;\"><strong><span style=\"color: #149191;\">\u062a\u0645\u0631\u06cc\u0646\u0627\u062a \u0641\u0635\u0644<\/span><\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>*1- \u06cc\u0627\u062f\u062a\u0627\u0646 \u0647\u0633\u062a \u06a9\u0647 \u06af\u0641\u062a\u0645 \u0627\u06af\u0631 $|\\psi \\rangle$ \u0648 $|\\phi \\rangle$ \u0648\u0627\u0628\u0633\u062a\u0647 \u062e\u0637\u06cc \u06cc\u06a9\u062f\u06cc\u06af\u0631 \u0628\u0627\u0634\u0646\u062f\u061b \u0646\u0627\u0645\u0633\u0627\u0648\u06cc \u0634\u0648\u0627\u0631\u062a\u0632 \u062a\u0628\u062f\u06cc\u0644 \u0628\u0647 \u062a\u0633\u0627\u0648\u06cc \u0645\u06cc \u0634\u0648\u062f\u061f \u0627\u06cc\u0646 \u0631\u0627 \u0627\u062b\u0628\u0627\u062a \u06a9\u0646\u06cc\u062f. \u0647\u0645\u06cc\u0646 \u0631\u0627 \u0628\u0631\u0627\u06cc \u0646\u0627\u0645\u0633\u0627\u0648\u06cc \u0645\u062b\u0644\u062b \u0646\u06cc\u0632 \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u062f.<\/p>\n<p>*2- \u062f\u0648 \u06a9\u062a \u0632\u06cc\u0631 \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u062f:<\/p>\n<p dir=\"ltr\" style=\"text-align: center;\">$| \\psi \\rangle = \\displaystyle{\\begin{bmatrix} -3i \\\\ 2+i \\\\ 4 \\end{bmatrix}} \\; , \\; | \\phi \\rangle =\\displaystyle{\\begin{bmatrix} 2 \\\\ -i \\\\ 2-3i \\end{bmatrix}}$<\/p>\n<p>\u0627\u0644\u0641) \u0628\u0631\u062f\u0627\u0631 \u0628\u0631\u0627 $\\langle \\phi |$ \u0631\u0627 \u0645\u062d\u0627\u0633\u0628\u0647 \u06a9\u0646\u06cc\u062f.<\/p>\n<p>\u0628) \u0636\u0631\u0628 \u062f\u0627\u062e\u0644\u06cc $\\langle \\phi | \\psi \\rangle$ \u0631\u0627 \u0628\u062f\u0633\u062a \u0622\u0648\u0631\u06cc\u062f.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u062d\u0627\u0644\u062a \u0641\u06cc\u0632\u06cc\u06a9\u06cc \u06cc\u06a9 \u0633\u0627\u0645\u0627\u0646\u0647 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645\u06cc\u060c \u0628\u0627 \u0639\u0646\u0635\u0631\u0647\u0627\u06cc \u0641\u0636\u0627\u06cc \u0647\u06cc\u0644\u0628\u0631\u062a \u0646\u0645\u0627\u06cc\u0634 \u0645\u06cc \u062f\u0647\u06cc\u0645. \u0627\u06cc\u0646 \u0639\u0646\u0627\u0635\u0631\u060c \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc \u062d\u0627\u0644\u062a \u0646\u0627\u0645\u06cc\u062f\u0647 \u0645\u06cc \u0634\u0648\u0646\u062f. \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc \u062d\u0627\u0644\u062a \u062f\u0631 \u067e\u0627\u06cc\u0647 \u0647\u0627\u06cc \u0645\u062a\u0641\u0627\u0648\u062a \u0628\u0648\u0633\u06cc\u0644\u0647 \u0628\u0633\u0637 \u062a\u0627\u0628\u0639 \u0647\u0627 \u0646\u0645\u0627\u06cc\u0634 \u067e\u0630\u06cc\u0631\u0646\u062f. \u0647\u0645\u0627\u0646\u0637\u0648\u0631 \u06a9\u0647 \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc \u0641\u0636\u0627\u06cc \u062f\u06a9\u0627\u0631\u062a\u06cc \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u062f\u0631 \u062f\u0633\u062a\u06af\u0627\u0647 \u0645\u062e\u062a\u0635\u0627\u062a \u0647\u0627\u06cc \u06af\u0648\u0646\u0627\u06af\u0648\u0646 (\u0645\u062b\u0644\u0627 \u0628\u0627 \u0627\u0646\u062f\u06a9\u06cc \u062f\u0648\u0631\u0627\u0646 \u0646\u0633\u0628\u062a \u0628\u0647 \u06cc\u06a9\u062f\u06cc\u06af\u0631) \u0646\u0645\u0627\u06cc\u0634 \u062f\u0627\u062f. \u0642\u0637\u0639\u0627 \u0628\u0631\u062f\u0627\u0631 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":304,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"https:\/\/cdn.imgurl.ir\/uploads\/e5796_screenshot_2023-08-14_200854_ppew.png","fifu_image_alt":"\u0646\u0645\u0627\u062f\u06af\u0630\u0627\u0631\u06cc \u062f\u06cc\u0631\u0627\u06a9","footnotes":""},"categories":[5,26],"tags":[28,27],"class_list":["post-303","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-physics","category-26","tag-28","tag-27"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>4 \u0646\u0645\u0627\u062f\u06af\u0630\u0627\u0631\u06cc \u062f\u06cc\u0631\u0627\u06a9 - 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\u0646\u0645\u0627\u062f\u06af\u0630\u0627\u0631\u06cc \u062f\u06cc\u0631\u0627\u06a9 - \u0633\u0627\u06cc\u0646\u0633\u06cc\u0648\" \/>\n<meta property=\"og:description\" content=\"\u0646\u0645\u0627\u062f\u06af\u0630\u0627\u0631\u06cc \u062f\u06cc\u0631\u0627\u06a9 \u0628\u0631\u0627\u06cc \u0627\u0633\u062a\u0642\u0644\u0627\u0644 \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc \u062d\u0627\u0644\u062a \u0627\u0632 \u0645\u062e\u062a\u0635\u0627\u062a\u060c \u062a\u0648\u0633\u0637 \u062f\u0627\u0646\u0634\u0645\u0646\u062f \u0634\u0647\u06cc\u0631 \u0645\u06a9\u0627\u0646\u06cc\u06a9 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645\u06cc\u060c \u067e\u0644 \u062f\u06cc\u0631\u0627\u06a9 \u062a\u0628\u06cc\u06cc\u0646 \u0634\u062f.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/sciencio.ir\/?p=303\" \/>\n<meta property=\"og:site_name\" content=\"\u0633\u0627\u06cc\u0646\u0633\u06cc\u0648\" \/>\n<meta property=\"article:published_time\" content=\"2026-08-12T04:06:33+00:00\" 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