{"id":296,"date":"2026-08-12T07:30:59","date_gmt":"2026-08-12T04:00:59","guid":{"rendered":"https:\/\/sciencio.ir\/?p=296"},"modified":"2026-08-12T07:30:59","modified_gmt":"2026-08-12T04:00:59","slug":"2-%d8%a8%d8%b9%d8%af-%d9%88-%d9%be%d8%a7%db%8c%d9%87-%d9%81%d8%b6%d8%a7%db%8c-%d8%a8%d8%b1%d8%af%d8%a7%d8%b1%db%8c","status":"publish","type":"post","link":"https:\/\/sciencio.ir\/?p=296","title":{"rendered":"2 \u0628\u0639\u062f \u0648 \u067e\u0627\u06cc\u0647 \u0641\u0636\u0627\u06cc \u0628\u0631\u062f\u0627\u0631\u06cc"},"content":{"rendered":"

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

1-2 \u0627\u0633\u062a\u0642\u0644\u0627\u0644 \u0648 \u0648\u0627\u0628\u0633\u062a\u06af\u06cc \u062e\u0637\u06cc<\/h3>\n

\u0628\u0647 \u0645\u062c\u0645\u0648\u0639\u0647 \u0627\u06cc \u0627\u0632 $N$ \u0628\u0631\u062f\u0627\u0631 \u0646\u0627\u0635\u0641\u0631 $\\phi_1,\\phi_2,…\\phi_N$ \u0645\u0633\u062a\u0642\u0644 \u062e\u0637\u06cc \u06af\u0648\u06cc\u06cc\u0645 \u0647\u0631\u06af\u0627\u0647 \u062a\u0646\u0647\u0627<\/strong> \u062c\u0648\u0627\u0628 \u0645\u0639\u0627\u062f\u0644\u0647 (1)\u060c \u062c\u0648\u0627\u0628\u06cc \u0627\u0633\u062a \u06a9\u0647 \u062f\u0631 \u0622\u0646 \u0647\u0645\u0647 \u0636\u0631\u0627\u06cc\u0628 \u0627\u0633\u06a9\u0627\u0644\u0631 \u0635\u0641\u0631 \u0628\u0627\u0634\u062f<\/p>\n

($a_1=a_2=…=a_N=0$):<\/p>\n

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

$\\large \\displaystyle{\\sum_{i=1}^{N}a_i\\phi_i}=O$<\/p>\n

\u062f\u0631 \u0631\u0627\u0628\u0637\u0647 \u0628\u0627\u0644\u0627 $O$ \u0628\u0647 \u0645\u0639\u0646\u0627\u06cc \u0628\u0631\u062f\u0627\u0631 \u0635\u0641\u0631 \u0627\u0633\u062a. \u0627\u0645\u0627 \u0627\u06af\u0631 \u06cc\u06a9 \u0645\u062c\u0645\u0648\u0639\u0647 \u0636\u0631\u0627\u06cc\u0628 \u0627\u0633\u06a9\u0627\u0644\u0631 $\\{a_i\\}$ \u0648\u062c\u0648\u062f \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f \u06a9\u0647 \u062a\u0645\u0627\u0645\u06cc \u0627\u0639\u0636\u0627\u06cc \u0622\u0646 \u0635\u0641\u0631 \u0646\u0628\u0627\u0634\u062f \u0648 \u062f\u0631 \u0645\u0639\u0627\u062f\u0644\u0647 \u0628\u0627\u0644\u0627 \u0635\u062f\u0642 \u06a9\u0646\u062f\u061b \u0628\u0631\u062f\u0627\u0631\u0647\u0627 \u0648\u0627\u0628\u0633\u062a\u0647 \u062e\u0637\u06cc \u0627\u0646\u062f. \u062f\u0631 \u0627\u06cc\u0646 \u0635\u0648\u0631\u062a \u0647\u0645\u0648\u0627\u0631\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646 \u06cc\u06a9\u06cc \u0627\u0632 \u0628\u0631\u062f\u0627\u0631\u0647\u0627 (\u0645\u062b\u0644\u0627 \u0627\u06cc\u0646\u062c\u0627 $\\phi_M$) \u0631\u0627 \u0628\u0647 \u0635\u0648\u0631\u062a \u062a\u0631\u06a9\u06cc\u0628 \u062e\u0637\u06cc \u0627\u0632 \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc \u062f\u06cc\u06af\u0631 \u0646\u0648\u0634\u062a:<\/p>\n

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

$\\large \\phi_M=\\displaystyle{\\sum_{i=1}^{M-1}a_i\\phi_i+\\sum_{i=M+1}^{N}a_i\\phi_i}$<\/p>\n

\u0628\u0627 \u0645\u062b\u0627\u0644 \u0627\u06cc\u0646 \u0645\u0628\u062d\u062b \u0631\u0648\u0634\u0646\u200c\u062a\u0631 \u0645\u06cc \u0634\u0648\u062f.<\/p>\n

*\u0645\u062b\u0627\u0644 63-1)<\/h5>\n

\u0645\u062c\u0645\u0648\u0639\u0647 \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc \u0632\u06cc\u0631 \u0648\u0627\u0628\u0633\u062a\u0647 \u062e\u0637\u06cc \u0627\u0646\u062f \u06cc\u0627 \u0645\u0633\u062a\u0642\u0644 \u062e\u0637\u06cc\u061f<\/p>\n

\u0627\u0644\u0641) $A=(2,0,0),B=(0,1,0),C=(0,0,-5)$<\/p>\n

\u0628) $A=(6,-9,0),B=(-2,3,0)$<\/p>\n

\u067e\u0627\u0633\u062e<\/h5>\n

\u0627\u0644\u0641)<\/strong><\/p>\n

\u0645\u0639\u0627\u062f\u0644\u0647 (1) \u0631\u0627 \u062a\u0634\u06a9\u06cc\u0644 \u0645\u06cc \u062f\u0647\u06cc\u0645 \u062a\u0627 \u0628\u0628\u06cc\u0646\u06cc\u0645 \u06a9\u0647 \u0636\u0631\u0627\u06cc\u0628 \u0627\u0633\u06a9\u0627\u0644\u0631 \u0686\u06af\u0648\u0646\u0647 \u0627\u0646\u062f:<\/p>\n

$\\large a_1A+a_2B+a_3C=O$<\/p>\n

$\\large (2a_1)\\hat{i}+(a_2)\\hat{j}+(-5a_3)\\hat{k}=O$<\/p>\n

\u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u0627\u06cc\u0646\u06a9\u0647 \u0647\u0631\u0633\u0647 \u0645\u0648\u0644\u0641\u0647 \u0628\u0627\u06cc\u062f \u0635\u0641\u0631 \u0628\u0627\u0634\u0646\u062f\u061b \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0636\u0631\u0627\u06cc\u0628 \u062c\u0645\u0644\u06af\u06cc \u0635\u0641\u0631\u0646\u062f$a_1=a_2=a_3=0$. \u0628\u062f\u06cc\u0646 \u062a\u0631\u062a\u06cc\u0628 \u0633\u0647 \u0628\u0631\u062f\u0627\u0631 \u0645\u0633\u062a\u0642\u0644 \u062e\u0637\u06cc \u0627\u0646\u062f.<\/p>\n

\u0628)<\/strong><\/p>\n

\u0647\u0645\u0627\u0646\u0646\u062f \u0627\u0644\u0641\u060c \u0645\u0639\u0627\u062f\u0644\u0647 (1) \u0631\u0627 \u062a\u0634\u06a9\u06cc\u0644 \u0645\u06cc \u062f\u0647\u06cc\u0645:<\/p>\n

$\\large (6a_1-2a_2)\\hat{i}+(-9a_1+3a_2)\\hat{j}=O$<\/p>\n

\u062d\u0627\u0644 \u0686\u0648\u0646 \u062f\u0648 \u0645\u0648\u0644\u0641\u0647 \u0635\u0641\u0631\u0646\u062f\u061b \u0627\u0632 \u0647\u0631 \u062f\u0648 \u0645\u0639\u0627\u062f\u0644\u0647 \u0628\u0647 \u0627\u06cc\u0646 \u062c\u0648\u0627\u0628 \u0645\u06cc \u0631\u0633\u06cc\u0645 $a_2=3a_1$. \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u062c\u0648\u0627\u0628 $a_1=a_2=0$ \u062a\u0646\u0647\u0627 \u062c\u0648\u0627\u0628 \u0645\u0639\u0627\u062f\u0644\u0647 (1) \u0646\u06cc\u0633\u062a \u0648 \u0628\u06cc \u0646\u0647\u0627\u06cc\u062a \u062c\u0648\u0627\u0628 \u062f\u06cc\u06af\u0631 \u0645\u0648\u062c\u0648\u062f\u0646\u062f \u067e\u0633 \u062f\u0648 \u0628\u0631\u062f\u0627\u0631 \u0648\u0627\u0628\u0633\u062a\u0647 \u062e\u0637\u06cc \u0627\u0646\u062f. \u0647\u0645\u0686\u0646\u06cc\u0646 \u0645\u06cc \u062a\u0648\u0627\u0646 \u06cc\u06a9 \u0628\u0631\u062f\u0627\u0631 \u0631\u0627 \u0628\u0631\u062d\u0633\u0628 \u0628\u0631\u062f\u0627\u0631 \u062f\u06cc\u06af\u0631 \u0646\u0648\u0634\u062a \u06a9\u0647 \u0627\u06cc\u0646 \u0646\u06cc\u0632 \u062e\u0627\u0635\u06cc\u062a \u0648\u0627\u0628\u0633\u062a\u06af\u06cc \u062e\u0637\u06cc \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u0633\u062a. $A=-3B$<\/p>\n

\n

2-2 \u0628\u0639\u062f<\/h3>\n

\u0628\u06cc\u0634\u062a\u0631\u06cc\u0646 \u062a\u0639\u062f\u0627\u062f \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc \u0645\u0633\u062a\u0642\u0644 \u062e\u0637\u06cc \u06a9\u0647 \u06cc\u06a9 \u0641\u0636\u0627\u06cc \u0628\u0631\u062f\u0627\u0631\u06cc \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f \u0631\u0627 \u0628\u0639\u062f \u0641\u0636\u0627 \u0645\u06cc \u06af\u0648\u06cc\u06cc\u0645. \u0627\u06af\u0631 \u0628\u06cc\u0634\u06cc\u0646\u0647 \u062a\u0639\u062f\u0627\u062f \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc \u0645\u0633\u062a\u0642\u0644 \u062e\u0637\u06cc $N$ \u0628\u0627\u0634\u062f\u061b \u0622\u0646 \u06af\u0627\u0647 \u0628\u0647 \u0627\u06cc\u0646 \u0641\u0636\u0627 $N$-\u0628\u0639\u062f\u06cc \u0645\u06cc \u06af\u0648\u06cc\u06cc\u0645. \u062f\u0631 \u0686\u0646\u06cc\u0646 \u0634\u0631\u0627\u06cc\u0637\u06cc \u0645\u06cc \u062a\u0648\u0627\u0646 \u0647\u0631 \u0628\u0631\u062f\u0627\u0631 \u062f\u0644\u062e\u0648\u0627\u0647 \u062f\u0631 \u0627\u06cc\u0646 \u0641\u0636\u0627\u06cc \u0628\u0631\u062f\u0627\u0631\u06cc – \u0645\u0627\u0646\u0646\u062f $\\psi$ – \u0631\u0627 \u0628\u0647 \u0635\u0648\u0631\u062a \u06cc\u06a9 \u062a\u0631\u06a9\u06cc\u0628 \u062e\u0637\u06cc (\u0636\u0631\u0627\u06cc\u0628 \u0627\u0633\u06a9\u0627\u0644\u0631 \u0628\u0631\u0627\u06cc \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc \u0645\u0633\u062a\u0642\u0644 \u062e\u0637\u06cc) \u0628\u0633\u0637 \u062f\u0627\u062f:<\/p>\n

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

$\\large \\psi=\\displaystyle{\\sum_{i=1}^{N}a_i\\phi_i}$<\/p>\n

3-2 \u067e\u0627\u06cc\u0647<\/h3>\n

\u0645\u062c\u0645\u0648\u0639\u0647 \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc \u0645\u0633\u062a\u0642\u0644 \u062e\u0637\u06cc ($\\phi_1,\\phi_2,…\\phi_N$) \u06a9\u0647 \u062a\u0639\u062f\u0627\u062f \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc \u0622\u0646 \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u0628\u0639\u062f \u0641\u0636\u0627\u06cc \u0628\u0631\u062f\u0627\u0631\u06cc \u0627\u0633\u062a\u061b \u067e\u0627\u06cc\u0647 \u0641\u0636\u0627\u06cc \u0628\u0631\u062f\u0627\u0631\u06cc \u0646\u0627\u0645\u06cc\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f \u0648 \u0628\u0647 \u0635\u0648\u0631\u062a $\\{\\phi_i\\}$ \u0646\u0645\u0627\u06cc\u0634 \u0645\u06cc \u062f\u0647\u06cc\u0645. \u0647\u0631 \u0628\u0631\u062f\u0627\u0631 \u0639\u0636\u0648 \u0627\u06cc\u0646 \u0645\u062c\u0645\u0648\u0639\u0647\u060c \u0628\u0631\u062f\u0627\u0631 \u067e\u0627\u06cc\u0647 \u0627\u0633\u062a. \u0627\u06af\u0631\u0686\u0647 \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc \u067e\u0627\u06cc\u0647 \u062f\u0644\u062e\u0648\u0627\u0647\u200c\u0627\u0646\u062f\u061b \u062e\u0648\u0628 \u0627\u0633\u062a \u06a9\u0647 \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc \u067e\u0627\u06cc\u0647 \u0645\u062a\u0639\u0627\u0645\u062f \u0628\u0647\u0646\u062c\u0627\u0631 \u0628\u0627\u0634\u0646\u062f. \u0645\u062a\u0639\u0627\u0645\u062f \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0639\u0646\u0627 \u06a9\u0647 \u0628\u0631\u0647\u0645 \u0639\u0645\u0648\u062f\u0646\u062f \u0648 \u0628\u0647\u0646\u062c\u0627\u0631 \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0639\u0646\u0627 \u06a9\u0647 \u0646\u0631\u0645 (\u0627\u0646\u062f\u0627\u0632\u0647 \u06cc\u0627 \u0637\u0648\u0644) \u0628\u0631\u062f\u0627\u0631 \u0648\u0627\u062d\u062f \u0627\u0633\u062a. \u062a\u0645\u0627\u0645 \u0645\u0641\u0647\u0648\u0645 \u0645\u062a\u0639\u0627\u0645\u062f \u0628\u0647\u0646\u062c\u0627\u0631 \u062f\u0631 \u0636\u0631\u0628 \u062f\u0627\u062e\u0644\u06cc \u0632\u06cc\u0631 \u0645\u06cc\u0627\u0646 \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc \u067e\u0627\u06cc\u0647 \u0642\u0627\u0628\u0644 \u0628\u06cc\u0627\u0646 \u0627\u0633\u062a:<\/p>\n

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

$\\large \\langle \\phi_i | \\phi_j \\rangle = \\delta_{ij}$<\/p>\n

\u06a9\u0647 $\\delta_{ij}$ \u062f\u0644\u062a\u0627\u06cc \u06a9\u0631\u0648\u0646\u06a9\u0631 \u0627\u0633\u062a. \u0647\u0631\u06af\u0627\u0647 $i=j$ \u0628\u0627\u0634\u062f \u0628\u0631\u0627\u0628\u0631 \u0628\u0627 \u06cc\u06a9 \u0648 \u062f\u0631 \u063a\u06cc\u0631 \u0627\u06cc\u0646\u0635\u0648\u0631\u062a \u0635\u0641\u0631 \u0627\u0633\u062a. \u0647\u0631\u06af\u0627\u0647 \u067e\u0627\u06cc\u0647 \u0627\u06cc \u062a\u0645\u0627\u0645 \u0641\u0636\u0627 \u0631\u0627 \u067e\u0648\u0634\u0634 \u062f\u0647\u062f (\u0647\u0645\u0647 \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc \u0641\u0636\u0627 \u062a\u0631\u06a9\u06cc\u0628 \u062e\u0637\u06cc \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc \u067e\u0627\u06cc\u0647 \u0628\u0627\u0634\u062f) \u0628\u0647 \u0622\u0646 \u067e\u0627\u06cc\u0647\u060c \u06a9\u0627\u0645\u0644 \u0645\u06cc \u06af\u0648\u06cc\u06cc\u0645. \u0636\u0631\u0627\u06cc\u0628 \u0628\u0633\u0637 $a_i$ \u062f\u0631 \u0631\u0627\u0628\u0637\u0647 (3) \u0646\u06cc\u0632 \u0645\u0648\u0644\u0641\u0647 \u0647\u0627\u06cc \u0628\u0631\u062f\u0627\u0631 $\\psi$ \u062f\u0631 \u0627\u06cc\u0646 \u067e\u0627\u06cc\u0647 \u0647\u0633\u062a\u0646\u062f \u06a9\u0647 \u0628\u0648\u0633\u06cc\u0644\u0647 $i$ \u0628\u0647 \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc \u067e\u0627\u06cc\u0647 \u0645\u0631\u0628\u0648\u0637 \u0645\u06cc \u0634\u0648\u0646\u062f. \u0647\u0631 \u0645\u0648\u0644\u0641\u0647 \u0627\u0632 \u0636\u0631\u0628 \u0646\u0631\u062f\u0647 \u0627\u06cc \u0628\u0631\u062f\u0627\u0631 \u067e\u0627\u06cc\u0647 \u062f\u0631 $\\psi$ \u0628\u062f\u0633\u062a \u0645\u06cc \u0622\u06cc\u062f (\u0645\u0634\u0627\u0628\u0647 \u062a\u0635\u0648\u06cc\u0631 \u06a9\u0631\u062f\u0646 \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc \u0639\u0627\u062f\u06cc \u0628\u0631 \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc \u067e\u0627\u06cc\u0647):<\/p>\n

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

$\\large\u00a0a_i = \\large \\langle \\phi_i | \\psi \\rangle $<\/p>\n

1-3-2 \u0645\u062b\u0627\u0644 \u0647\u0627\u06cc\u06cc \u0627\u0632 \u0641\u0636\u0627\u06cc \u0628\u0631\u062f\u0627\u0631\u06cc \u062e\u0637\u06cc<\/h5>\n

\u0645\u06cc \u062e\u0648\u0627\u0647\u0645 \u062f\u0648 \u0645\u062b\u0627\u0644 \u0627\u0632 \u0641\u0636\u0627\u0647\u0627\u06cc \u0628\u0631\u062f\u0627\u0631\u06cc \u062e\u0637\u06cc \u0627\u0631\u0627\u0626\u0647 \u06a9\u0646\u0645 \u06a9\u0647 \u0647\u0631\u062f\u0648 \u0641\u0636\u0627\u06cc \u0647\u06cc\u0644\u0628\u0631\u062a \u0647\u0633\u062a\u0646\u062f: \u06cc\u06a9\u06cc \u0645\u062c\u0645\u0648\u0639\u0647 \u0645\u062a\u0646\u0627\u0647\u06cc (\u06af\u0633\u0633\u062a\u0647) \u0627\u0632 \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc \u067e\u0627\u06cc\u0647 \u0648 \u062f\u06cc\u06af\u0631\u06cc \u067e\u0627\u06cc\u0647 \u0646\u0627\u0645\u062a\u0646\u0627\u0647\u06cc (\u067e\u06cc\u0648\u0633\u062a\u0647) \u062f\u0627\u0631\u062f.<\/p>\n

    \n
  • \u0641\u0636\u0627\u06cc \u0633\u0647 \u0628\u0639\u062f\u06cc \u062f\u06a9\u0627\u0631\u062a\u06cc\u060c \u067e\u0627\u06cc\u0647 \u0627\u06cc\u0646 \u0641\u0636\u0627 \u0627\u0632 \u0633\u0647 \u0628\u0631\u062f\u0627\u0631 \u0645\u0633\u062a\u0642\u0644 \u062e\u0637\u06cc $\\hat{i}$\u060c $\\hat{j}$ \u0648 $\\hat{k}$ \u062a\u0634\u06a9\u06cc\u0644 \u0634\u062f\u0647 \u0627\u0633\u062a. \u062f\u0631 \u0641\u0635\u0648\u0644 \u0642\u0628\u0644 \u0628\u0627 \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u0627\u06cc\u0646 \u0641\u0636\u0627 \u0622\u0634\u0646\u0627 \u0634\u062f\u06cc\u0645.<\/li>\n
  • \u0641\u0636\u0627\u06cc \u062a\u0645\u0627\u0645 \u062a\u0648\u0627\u0628\u0639 \u0645\u062e\u062a\u0644\u0637 $\\psi (x)$\u060c \u0628\u0639\u062f \u0627\u06cc\u0646 \u0641\u0636\u0627 \u0646\u0627\u0645\u062a\u0646\u0627\u0647\u06cc \u0627\u0633\u062a \u0632\u06cc\u0631 \u067e\u0627\u06cc\u0647 \u0627\u0632 \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc(\u062a\u0648\u0627\u0628\u0639) \u0645\u0633\u062a\u0642\u0644 \u062e\u0637\u06cc \u0628\u06cc\u0634\u0645\u0627\u0631\u06cc \u062a\u0634\u06a9\u06cc\u0644 \u0634\u062f\u0647 \u0627\u0633\u062a.<\/li>\n<\/ul>\n
    *\u0645\u062b\u0627\u0644 2-2)<\/h5>\n

    \u062f\u0631 \u0645\u062c\u0645\u0648\u0639\u0647 \u0627\u06cc \u0627\u0632 \u062a\u0648\u0627\u0628\u0639\u060c \u0647\u0645\u0627\u0646\u0646\u062f \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u060c \u0647\u0646\u06af\u0627\u0645\u06cc \u06a9\u0647 \u0628\u062a\u0648\u0627\u0646 \u0647\u0631\u062a\u0627\u0628\u0639 \u0631\u0627 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u062a\u0631\u06a9\u06cc\u0628 \u062e\u0637\u06cc \u062f\u06cc\u06af\u0631 \u062a\u0648\u0627\u0628\u0639 (\u062c\u0645\u0639 \u062a\u0648\u0627\u0628\u0639 \u0628\u0627 \u0636\u0631\u0627\u06cc\u0628 \u0627\u0633\u06a9\u0627\u0644\u0631 \u06a9\u0647 \u062d\u062f\u0627\u0642\u0644 \u06cc\u06a9\u06cc \u0627\u0632 \u0636\u0631\u0627\u06cc\u0628 \u0635\u0641\u0631 \u0646\u0628\u0627\u0634\u062f) \u062a\u0639\u0631\u06cc\u0641 \u06a9\u0631\u062f\u061b \u0645\u06cc \u06af\u0648\u06cc\u06cc\u0645 \u062a\u0648\u0627\u0628\u0639 \u0648\u0627\u0628\u0633\u062a\u0647 \u062e\u0637\u06cc \u0648 \u062f\u0631 \u063a\u06cc\u0631 \u0627\u06cc\u0646 \u0635\u0648\u0631\u062a \u0645\u0633\u062a\u0642\u0644 \u062e\u0637\u06cc \u0647\u0633\u062a\u0646\u062f. \u062d\u0627\u0644 \u0628\u0631\u0631\u0633\u06cc \u06a9\u0646\u06cc\u062f \u06a9\u0647 \u0645\u062c\u0645\u0648\u0639\u0647 \u062a\u0648\u0627\u0628\u0639 \u0627\u0644\u0641 \u0648 \u0628 \u0628\u0631 \u0631\u0648\u06cc \u0645\u062d\u0648\u0631 \u062d\u0642\u06cc\u0642\u06cc $x$\u060c \u0645\u0633\u062a\u0642\u0644 \u062e\u0637\u06cc \u0627\u0646\u062f \u06cc\u0627 \u0648\u0627\u0628\u0633\u062a\u0647 \u062e\u0637\u06cc.<\/p>\n

    \u0627\u0644\u0641)$f(x)=4,g(x)=x^2,h(x)=e^{2x}$<\/p>\n

    \u0628)$f(x)=2+x^2,g(x)=3-x+4x^3,h(x)=2x+3x^2-8x^3$<\/p>\n

    \u067e\u0627\u0633\u062e<\/h5>\n

    \u0627\u0644\u0641)<\/strong><\/p>\n

    \u0647\u06cc\u0686 \u06a9\u062f\u0627\u0645 \u0627\u0632 \u062a\u0648\u0627\u0628\u0639 \u0627\u0644\u0641 \u0631\u0627 \u0646\u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0631\u062d\u0633\u0628 \u062f\u06cc\u06af\u0631\u06cc \u0646\u0648\u0634\u062a. \u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u062a\u0648\u0627\u0628\u0639 \u0645\u0633\u062a\u0642\u0644 \u062e\u0637\u06cc \u0627\u0646\u062f. \u0628\u0635\u0648\u0631\u062a \u0645\u0639\u0627\u062f\u0644\u060c \u062a\u0633\u0627\u0648\u06cc \u0632\u06cc\u0631 \u062a\u0646\u0647\u0627 \u06cc\u06a9 \u062c\u0648\u0627\u0628 \u062f\u0627\u0631\u062f \u0648 \u0622\u0646 \u0647\u0645 \u0632\u0645\u0627\u0646\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0636\u0631\u0627\u06cc\u0628 $a_i$ \u0647\u0645\u06af\u06cc \u0635\u0641\u0631 \u0628\u0627\u0634\u0646\u062f:<\/p>\n

    $\\large a_1(4)+a_2(x^2)+a_3(e^{2x})=0$<\/p>\n

    \u0628)<\/strong><\/p>\n

    \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u062f \u06a9\u0647 $h(x)=3f(x)-2g(x)$ \u0628\u0631\u0642\u0631\u0627\u0631 \u0627\u0633\u062a. \u067e\u0633 \u062a\u0648\u0627\u0628\u0639 \u0628 \u0648\u0627\u0628\u0633\u062a\u0647 \u062e\u0637\u06cc \u0627\u0646\u062f.<\/p>\n

    \n

    4-63 \u062c\u0645\u0639 \u0628\u0646\u062f\u06cc \u0641\u0635\u0644<\/h3>\n

    \u062f\u0631 \u0627\u06cc\u0646 \u0641\u0635\u0644 \u0628\u0627 \u0622\u0634\u0646\u0627\u06cc\u06cc \u0628\u0627 \u0627\u0633\u062a\u0642\u0644\u0627\u0644 \u0648 \u0648\u0627\u0628\u0633\u062a\u06af\u06cc \u062e\u0637\u06cc\u060c \u0628\u0639\u062f \u0648 \u067e\u0627\u06cc\u0647 \u0641\u0636\u0627\u06cc \u0628\u0631\u062f\u0627\u0631\u06cc \u06cc\u06a9 \u0642\u062f\u0645 \u0631\u0648\u0628\u0647 \u062c\u0644\u0648 \u062f\u0631 \u0622\u0634\u0646\u0627\u06cc\u06cc \u0628\u0627 \u0645\u06a9\u0627\u0646\u06cc\u06a9 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645\u06cc \u0628\u0631\u062f\u0627\u0634\u062a\u06cc\u0645.<\/p>\n","protected":false},"excerpt":{"rendered":"

    \u062f\u0631 \u0641\u0635\u0644 \u0642\u0628\u0644 \u0628\u0627 \u0641\u0636\u0627\u06cc \u0647\u06cc\u0644\u0628\u0631\u062a \u0622\u0634\u0646\u0627 \u0634\u062f\u06cc\u0645. \u062f\u0631 \u0627\u06cc\u0646 \u0641\u0635\u0644\u060c \u0627\u0628\u062a\u062f\u0627 \u0645\u0641\u0647\u0648\u0645 \u0627\u0633\u062a\u0642\u0644\u0627\u0644 \u0648 \u0648\u0627\u0628\u0633\u062a\u06af\u06cc \u062e\u0637\u06cc \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f. \u0633\u067e\u0633 \u0628\u0639\u062f \u0648 \u067e\u0627\u06cc\u0647 \u06cc\u06a9 \u0641\u0636\u0627\u06cc \u0628\u0631\u062f\u0627\u0631\u06cc \u0631\u0627 \u062a\u0648\u0636\u06cc\u062d \u062e\u0648\u0627\u0647\u0645 \u062f\u0627\u062f \u062a\u0627 \u0628\u06cc\u0634\u062a\u0631 \u0628\u0627 \u0627\u0628\u0632\u0627\u0631\u0647\u0627\u06cc \u0631\u06cc\u0627\u0636\u06cc \u0645\u06a9\u0627\u0646\u06cc\u06a9 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645 \u0622\u0634\u0646\u0627 \u0634\u0648\u06cc\u0645. 1-2 \u0627\u0633\u062a\u0642\u0644\u0627\u0644 \u0648 \u0648\u0627\u0628\u0633\u062a\u06af\u06cc \u062e\u0637\u06cc \u0628\u0647 \u0645\u062c\u0645\u0648\u0639\u0647 \u0627\u06cc \u0627\u0632 $N$ \u0628\u0631\u062f\u0627\u0631 \u0646\u0627\u0635\u0641\u0631 $\\phi_1,\\phi_2,…\\phi_N$ \u0645\u0633\u062a\u0642\u0644 […]<\/p>\n","protected":false},"author":1,"featured_media":297,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"https:\/\/cdn.imgurl.ir\/uploads\/a704185_orthogonal-versus-orthonormal-vectors.width-1200_5mpz.jpg","fifu_image_alt":"\u0628\u0639\u062f \u0648 \u067e\u0627\u06cc\u0647 \u0641\u0636\u0627\u06cc \u0628\u0631\u062f\u0627\u0631\u06cc","footnotes":""},"categories":[5,26],"tags":[28,27],"class_list":["post-296","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-physics","category-26","tag-28","tag-27"],"yoast_head":"\n2 \u0628\u0639\u062f \u0648 \u067e\u0627\u06cc\u0647 \u0641\u0636\u0627\u06cc \u0628\u0631\u062f\u0627\u0631\u06cc - \u0633\u0627\u06cc\u0646\u0633\u06cc\u0648<\/title>\n<meta name=\"description\" content=\"\u062f\u0631 \u0641\u0635\u0644 \u0642\u0628\u0644 \u0628\u0627 \u0641\u0636\u0627\u06cc \u0647\u06cc\u0644\u0628\u0631\u062a \u0622\u0634\u0646\u0627 \u0634\u062f\u06cc\u0645. \u062f\u0631 \u0627\u06cc\u0646 \u0641\u0635\u0644\u060c \u0627\u0628\u062a\u062f\u0627 \u0645\u0641\u0647\u0648\u0645 \u0627\u0633\u062a\u0642\u0644\u0627\u0644 \u0648 \u0648\u0627\u0628\u0633\u062a\u06af\u06cc \u062e\u0637\u06cc \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u0648 \u0633\u067e\u0633 \u0628\u0639\u062f \u0648 \u067e\u0627\u06cc\u0647 \u0641\u0636\u0627\u06cc \u0628\u0631\u062f\u0627\u0631\u06cc \u0631\u0627 \u062a\u0648\u0636\u06cc\u062d \u0645\u06cc\u062f\u0647\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=296\" \/>\n<meta property=\"og:locale\" content=\"fa_IR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"2 \u0628\u0639\u062f \u0648 \u067e\u0627\u06cc\u0647 \u0641\u0636\u0627\u06cc \u0628\u0631\u062f\u0627\u0631\u06cc - \u0633\u0627\u06cc\u0646\u0633\u06cc\u0648\" \/>\n<meta property=\"og:description\" content=\"\u062f\u0631 \u0641\u0635\u0644 \u0642\u0628\u0644 \u0628\u0627 \u0641\u0636\u0627\u06cc \u0647\u06cc\u0644\u0628\u0631\u062a \u0622\u0634\u0646\u0627 \u0634\u062f\u06cc\u0645. \u062f\u0631 \u0627\u06cc\u0646 \u0641\u0635\u0644\u060c \u0627\u0628\u062a\u062f\u0627 \u0645\u0641\u0647\u0648\u0645 \u0627\u0633\u062a\u0642\u0644\u0627\u0644 \u0648 \u0648\u0627\u0628\u0633\u062a\u06af\u06cc \u062e\u0637\u06cc \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u0648 \u0633\u067e\u0633 \u0628\u0639\u062f \u0648 \u067e\u0627\u06cc\u0647 \u0641\u0636\u0627\u06cc 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