{"id":293,"date":"2026-08-12T07:28:14","date_gmt":"2026-08-12T03:58:14","guid":{"rendered":"https:\/\/sciencio.ir\/?p=293"},"modified":"2026-08-12T07:31:21","modified_gmt":"2026-08-12T04:01:21","slug":"1-%d9%81%d8%b6%d8%a7%db%8c-%d9%87%db%8c%d9%84%d8%a8%d8%b1%d8%aa","status":"publish","type":"post","link":"https:\/\/sciencio.ir\/?p=293","title":{"rendered":"1 \u0641\u0636\u0627\u06cc \u0647\u06cc\u0644\u0628\u0631\u062a"},"content":{"rendered":"<p>\u062f\u0631 \u0633\u0644\u0633\u0644\u0647 \u0641\u0635\u0644 \u0647\u0627\u06cc\u06cc \u0628\u0647 \u0645\u0641\u0627\u0647\u06cc\u0645 \u0648 \u0645\u0637\u0627\u0644\u0628 \u0645\u06a9\u0627\u0646\u06cc\u06a9 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645 \u0645\u06cc \u067e\u0631\u062f\u0627\u0632\u0645. \u0628\u0631\u0627\u06cc \u0627\u06cc\u0646\u06a9\u0647 \u062f\u0633\u062a\u06cc\u0627\u0628\u06cc \u0628\u0647 \u0645\u0637\u0627\u0644\u0628 \u0633\u0627\u062f\u0647 \u062a\u0631 \u0628\u0627\u0634\u062f\u061b \u0641\u0635\u0644 \u0647\u0627 \u06a9\u0648\u062a\u0627\u0647 \u062a\u0631\u0646\u062f \u062a\u0627 \u0639\u0646\u0627\u0648\u06cc\u0646 \u0645\u062a\u0645\u0627\u06cc\u0632 \u0648 \u062f\u0631 \u062f\u0633\u062a\u0631\u0633 \u0628\u0627\u0634\u0646\u062f. \u0645\u0639\u0627\u062f\u0644\u0647 \u0634\u0631\u0648\u062f\u06cc\u0646\u06af\u0631 \u06a9\u0647 \u0628\u0646\u06cc\u0627\u0646 \u0645\u06a9\u0627\u0646\u06cc\u06a9 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645 \u0628\u0631 \u0622\u0646 \u0627\u0633\u062a\u0648\u0627\u0631 \u0627\u0633\u062a\u061b \u0645\u0639\u0627\u062f\u0644\u0647 \u0627\u06cc \u062e\u0637\u06cc \u0627\u0633\u062a. \u0635\u0648\u0631\u062a \u0628\u0646\u062f\u06cc \u0645\u06a9\u0627\u0646\u06cc\u06a9 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645\u06cc \u0628\u0647 \u0639\u0645\u0644\u06af\u0631\u0647\u0627\u06cc \u062e\u0637\u06cc \u0645\u06cc \u067e\u0631\u062f\u0627\u0632\u062f \u0648 \u0628\u0627 \u062a\u0648\u0627\u0628\u0639 \u0645\u0648\u062c\u06cc \u0633\u0631\u0648\u06a9\u0627\u0631 \u062f\u0627\u0631\u062f \u06a9\u0647 \u0628\u0647 \u0641\u0636\u0627\u06cc \u0627\u0646\u062a\u0632\u0627\u0639\u06cc \u0647\u06cc\u0644\u0628\u0631\u062a \u0645\u062a\u0639\u0644\u0642 \u0647\u0633\u062a\u0646\u062f. \u0628\u062f\u06cc\u0646 \u062a\u0631\u062a\u06cc\u0628 \u0634\u0646\u0627\u062e\u062a \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u0631\u06cc\u0627\u0636\u06cc \u0648 \u0633\u0627\u062e\u062a\u0627\u0631 \u0641\u0636\u0627\u06cc \u0647\u06cc\u0644\u0628\u0631\u062a \u0628\u0631\u0627\u06cc \u062f\u0631\u06a9 \u0645\u06a9\u0627\u0646\u06cc\u06a9 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645\u06cc \u0636\u0631\u0648\u0631\u06cc \u0627\u0633\u062a.<\/p>\n<h3>1-1 \u0641\u0636\u0627\u06cc \u0628\u0631\u062f\u0627\u0631\u06cc \u062e\u0637\u06cc<\/h3>\n<p>\u0628\u0631\u0627\u06cc \u062f\u0631\u06a9 \u0641\u0636\u0627\u06cc \u0647\u06cc\u0644\u0628\u0631\u062a\u060c \u0646\u06cc\u0627\u0632 \u0628\u0647 \u062a\u0639\u0631\u06cc\u0641 \u0641\u0636\u0627\u06cc \u0628\u0631\u062f\u0627\u0631\u06cc \u062e\u0637\u06cc \u062f\u0627\u0631\u06cc\u0645. \u0641\u0636\u0627\u06cc \u0628\u0631\u062f\u0627\u0631\u06cc \u062e\u0637\u06cc \u0627\u0632 \u062f\u0648 \u0645\u062c\u0645\u0648\u0639\u0647 \u0639\u0646\u0627\u0635\u0631 \u0648 \u062f\u0648 \u0642\u0627\u0639\u062f\u0647 \u062c\u0628\u0631\u06cc \u062a\u0634\u06a9\u06cc\u0644 \u0645\u06cc \u0634\u0648\u062f. \u06cc\u06a9 \u0645\u062c\u0645\u0648\u0639\u0647 \u0627\u0632 \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc $\\psi$\u060c $\\phi$\u060c $\\chi$ \u0648&#8230; \u0648 \u06cc\u06a9 \u0645\u062c\u0645\u0648\u0639\u0647 \u0627\u0632 \u0627\u0633\u06a9\u0627\u0644\u0631\u0647\u0627\u06cc $a$\u060c $b$\u060c $c$ \u0648&#8230; \u0639\u0646\u0627\u0635\u0631 \u0641\u0636\u0627 \u0647\u0633\u062a\u0646\u062f. \u06cc\u06a9 \u0642\u0627\u0639\u062f\u0647 \u062c\u0628\u0631\u06cc \u062c\u0645\u0639 \u0628\u0631\u062f\u0627\u0631\u06cc \u0627\u0633\u062a \u0648 \u062f\u06cc\u06af\u0631 \u0642\u0627\u0639\u062f\u0647\u060c \u0636\u0631\u0628 \u0627\u0633\u06a9\u0627\u0644\u0631 \u062f\u0631 \u0628\u0631\u062f\u0627\u0631 \u0627\u0633\u062a.<\/p>\n<h5>1-1-1 \u0642\u0627\u0639\u062f\u0647 \u062c\u0645\u0639<\/h5>\n<p>\u0642\u0627\u0639\u062f\u0647 \u062c\u0645\u0639 \u0634\u0627\u0645\u0644 \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u0632\u06cc\u0631 \u0627\u0633\u062a:<\/p>\n<ul>\n<li>\u0627\u06af\u0631 $\\psi$ \u0648 $\\phi$ \u0628\u0631\u062f\u0627\u0631\u0647\u0627 (\u0639\u0646\u0627\u0635\u0631) \u06cc\u06a9 \u0641\u0636\u0627 \u0628\u0627\u0634\u0646\u062f\u061b \u062c\u0645\u0639 \u0622\u0646 \u0647\u0627 $\\psi+\\phi$ \u0646\u06cc\u0632 \u0628\u0631\u062f\u0627\u0631\u06cc \u062f\u0631 \u0647\u0645\u0627\u0646 \u0641\u0636\u0627\u0633\u062a.<\/li>\n<li>\u062c\u0645\u0639 \u062c\u0627\u0628\u062c\u0627\u06cc\u06cc \u067e\u0630\u06cc\u0631 \u0627\u0633\u062a: $\\psi+\\phi=\\phi+\\psi$<\/li>\n<li>\u062c\u0645\u0639 \u0634\u0631\u06a9\u062a \u067e\u0630\u06cc\u0631 \u0627\u0633\u062a: $(\\psi+\\phi)+\\chi=\\psi+(\\phi+\\chi)$<\/li>\n<li>\u0628\u0647 \u0627\u0632\u0627\u06cc \u0647\u0631 \u0628\u0631\u062f\u0627\u0631 $\\psi$\u060c \u06cc\u06a9 \u0628\u0631\u062f\u0627\u0631 \u0635\u0641\u0631 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f: $\\psi+O=O+\\psi=\\psi$<\/li>\n<li>\u0628\u0647 \u0627\u0632\u0627\u06cc \u0647\u0631 \u0628\u0631\u062f\u0627\u0631 $\\psi$ \u06cc\u06a9 \u0628\u0631\u062f\u0627\u0631 \u0645\u062a\u0642\u0627\u0631\u0646 (\u0642\u0631\u06cc\u0646\u0647) \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06a9\u0647 \u062c\u0645\u0639 \u0628\u0627 \u0622\u0646 \u0635\u0641\u0631 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f: $\\psi+(-\\psi)=(-\\psi)+\\psi=O$<\/li>\n<\/ul>\n<h5>2-1-1 \u0642\u0627\u0639\u062f\u0647 \u0636\u0631\u0628 \u0627\u0633\u06a9\u0627\u0644\u0631 \u062f\u0631 \u0628\u0631\u062f\u0627\u0631<\/h5>\n<p>\u0627\u0633\u06a9\u0627\u0644\u0631 \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u06cc\u06a9 \u0639\u062f\u062f \u062d\u0642\u06cc\u0642\u06cc \u06cc\u0627 \u0645\u062e\u062a\u0644\u0637 \u0628\u0627\u0634\u062f. \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u0632\u06cc\u0631\u060c \u0642\u0627\u0639\u062f\u0647 \u0636\u0631\u0628 \u0631\u0627 \u0645\u06cc \u0633\u0627\u0632\u0646\u062f:<\/p>\n<ul>\n<li>\u0636\u0631\u0628 \u0627\u0633\u06a9\u0627\u0644\u0631 \u062f\u0631 \u0628\u0631\u062f\u0627\u0631\u060c \u0628\u0631\u062f\u0627\u0631 \u062f\u06cc\u06af\u0631\u06cc \u062f\u0631 \u0647\u0645\u0627\u0646 \u0641\u0636\u0627 \u0628\u062f\u0633\u062a \u0645\u06cc \u062f\u0647\u062f. \u0627\u06af\u0631 $\\psi$ \u0648 $\\phi$ \u062f\u0648 \u0628\u0631\u062f\u0627\u0631 \u062f\u0631 \u06cc\u06a9 \u0641\u0636\u0627 \u0628\u0627\u0634\u0646\u062f \u0648 $a$ \u0648 $b$ \u062f\u0648 \u0627\u0633\u06a9\u0627\u0644\u0631\u061b \u0622\u0646\u06af\u0627\u0647 \u0647\u0631 \u062a\u0631\u06a9\u06cc\u0628 \u062e\u0637\u06cc $a\\psi+b\\phi$ \u0646\u06cc\u0632 \u0628\u0631\u062f\u0627\u0631 \u062f\u0631 \u0622\u0646 \u0641\u0636\u0627\u0633\u062a.<\/li>\n<li>\u062a\u0648\u0632\u06cc\u0639 \u067e\u0630\u06cc\u0631\u06cc \u0646\u0633\u0628\u062a \u0628\u0647 \u062c\u0645\u0639 \u0628\u0631\u0642\u0631\u0627\u0631 \u0627\u0633\u062a: $(a+b)\\psi=a\\psi+b\\psi \\;,\\; a(\\psi+\\phi)=a\\psi+a\\phi$<\/li>\n<li>\u0634\u0631\u06a9\u062a \u067e\u0630\u06cc\u0631\u06cc \u0646\u0633\u0628\u062a \u0628\u0647 \u0636\u0631\u0628 \u0627\u0633\u06a9\u0627\u0644\u0631\u0647\u0627 \u0628\u0631\u0642\u0631\u0627\u0631 \u0627\u0633\u062a: $a(b\\psi)=(ab)\\psi$<\/li>\n<li>\u0628\u0647 \u0627\u0632\u0627\u06cc \u0647\u0631 \u0628\u0631\u062f\u0627\u0631 $\\psi$\u060c \u0627\u0633\u06a9\u0627\u0644\u0631 \u06cc\u06a9\u0647 $I$ \u0648 \u0627\u0633\u06a9\u0627\u0644\u0631 \u0635\u0641\u0631 $o$ \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f: $\\psi I=I \\psi =\\psi \\; , \\; \\psi o = o \\psi=o$<\/li>\n<\/ul>\n<h3>2-1 \u0641\u0636\u0627\u06cc \u0647\u06cc\u0644\u0628\u0631\u062a<\/h3>\n<p>\u0641\u0631\u0636 \u06a9\u0646\u06cc\u062f \u06a9\u0647 \u0641\u0636\u0627\u06cc \u0647\u06cc\u0644\u0628\u0631\u062a \u0627\u0632 \u06cc\u06a9 \u0645\u062c\u0645\u0648\u0639\u0647 \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc $\\psi$\u060c $\\phi$\u060c $\\chi$ \u0648&#8230; \u0648 \u06cc\u06a9 \u0645\u062c\u0645\u0648\u0639\u0647 \u0627\u0632 \u0627\u0633\u06a9\u0627\u0644\u0631\u0647\u0627\u06cc $a$\u060c $b$\u060c $c$ \u0648&#8230; \u062a\u0634\u06a9\u06cc\u0644 \u0634\u062f\u0647 \u0627\u0633\u062a. \u062f\u0631 \u0641\u06cc\u0632\u06cc\u06a9 \u0641\u0636\u0627\u06cc \u0647\u06cc\u0644\u0628\u0631\u062a \u0631\u0627 \u0628\u0627 \u0646\u0645\u0627\u062f $\\mathcal{H}$ \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u06cc\u0645. \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u0632\u06cc\u0631 \u0645\u0639\u0631\u0641 \u06cc\u06a9 \u0641\u0636\u0627\u06cc \u0647\u06cc\u0644\u0628\u0631\u062a \u0627\u0633\u062a:<\/p>\n<ul>\n<li>\u0641\u0636\u0627\u06cc \u0647\u06cc\u0644\u0628\u0631\u062a \u06cc\u06a9 \u0641\u0636\u0627\u06cc \u0628\u0631\u062f\u0627\u0631\u06cc \u062e\u0637\u06cc \u0627\u0633\u062a.<\/li>\n<li>\u0628\u0631\u0627\u06cc \u0647\u0631 \u062f\u0648 \u0628\u0631\u062f\u0627\u0631 \u062f\u0631 \u0641\u0636\u0627\u06cc \u0647\u06cc\u0644\u0628\u0631\u062a &#8211; \u0645\u0627\u0646\u0646\u062f $\\psi$ \u0648 $\\phi$ &#8211; \u0647\u0645\u0648\u0627\u0631\u0647 \u0636\u0631\u0628 \u062f\u0627\u062e\u0644\u06cc \u062a\u0639\u0631\u06cc\u0641 \u0645\u06cc \u0634\u0648\u062f. \u0646\u062a\u06cc\u062c\u0647 \u0627\u06cc\u0646 \u0636\u0631\u0628 \u062f\u0627\u062e\u0644\u06cc \u0647\u0645\u0648\u0627\u0631\u0647 \u0645\u062a\u0646\u0627\u0647\u06cc \u0627\u0633\u062a. \u062d\u0627\u0635\u0644 \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u062d\u0642\u06cc\u0642\u06cc \u06cc\u0627 \u0645\u062e\u062a\u0644\u0637 \u0628\u0627\u0634\u062f. \u0636\u0631\u0628 \u062f\u0627\u062e\u0644\u06cc \u0627\u06cc\u0646 \u062f\u0648 \u062a\u0627\u0628\u0639 \u0631\u0627 \u0628\u0635\u0648\u0631\u062a $\\langle \\psi | \\phi \\rangle$ \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u06cc\u0645. \u0636\u0631\u0628 \u062f\u0627\u062e\u0644\u06cc \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u0632\u06cc\u0631 \u0631\u0627 \u062f\u0627\u0631\u0627\u0633\u062a:<\/li>\n<\/ul>\n<p>\u0636\u0631\u0628 \u062f\u0627\u062e\u0644\u06cc \u062f\u0648 \u0628\u0631\u062f\u0627\u0631 \u0628\u0647 \u0627\u06cc\u0646 \u0635\u0648\u0631\u062a \u0627\u0633\u062a \u06a9\u0647 \u0627\u0632 \u062f\u0631\u0627\u06cc\u0647 \u0647\u0627\u06cc \u0628\u0631\u062f\u0627\u0631 \u0627\u0648\u0644 \u0645\u0632\u062f\u0648\u062c \u0645\u062e\u062a\u0644\u0637 \u0645\u06cc \u06af\u06cc\u0631\u06cc\u0645 \u0648 \u0633\u067e\u0633 \u062f\u0631\u0627\u06cc\u0647 \u0647\u0627 \u0646\u0638\u06cc\u0631 \u0628\u0647 \u0646\u0638\u06cc\u0631 \u062f\u0631 \u0647\u0645 \u0636\u0631\u0628 \u0648 \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u0647\u0627 \u0628\u0627 \u06cc\u06a9\u062f\u06cc\u06af\u0631 \u062c\u0645\u0639 \u0645\u06cc \u0634\u0648\u0646\u062f.<\/p>\n<p><strong>(1)<\/strong><\/p>\n<p dir=\"ltr\" style=\"text-align: center;\">$\\large \\langle \\psi | \\phi \\rangle= \\psi^{*}.\\phi=\\psi^{*}_1\\phi_1+\\psi^{*}_2\\phi_2+&#8230;+\\psi^{*}_n\\phi_n$<\/p>\n<p>\u0628\u0627\u062a\u0648\u062c\u0647 \u0628\u0647 \u062e\u0627\u0635\u06cc\u062a \u0628\u0627\u0644\u0627\u060c \u062a\u0631\u062a\u06cc\u0628 \u062f\u0631 \u0636\u0631\u0628 \u062f\u0627\u062e\u0644\u06cc \u062f\u0627\u0631\u0627\u06cc \u0627\u0647\u0645\u06cc\u062a \u0627\u0633\u062a. \u0686\u0648\u0646 $ \\langle \\phi | \\psi \\rangle= \\phi^{*}.\\psi$\u060c \u062c\u0627\u0628\u062c\u0627\u06a9\u0631\u062f\u0646 \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u060c \u0627\u0632 \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u062f\u0627\u062e\u0644\u06cc \u0645\u0632\u062f\u0648\u062c \u0645\u062e\u062a\u0644\u0637 \u0645\u06cc \u06af\u06cc\u0631\u062f:<\/p>\n<p><strong>(2)<\/strong><\/p>\n<p dir=\"ltr\" style=\"text-align: center;\">$\\large \\langle \\psi | \\phi \\rangle= \\langle \\phi | \\psi \\rangle^{*}$<\/p>\n<ul>\n<li>\u0636\u0631\u0628 \u062f\u0627\u062e\u0644\u06cc \u0646\u0633\u0628\u062a \u0628\u0647 \u0639\u0627\u0645\u0644 \u062f\u0648\u0645 \u062e\u0637\u06cc \u0627\u0633\u062a\u061b \u06cc\u0639\u0646\u06cc \u0636\u0631\u0628 \u062f\u0627\u062e\u0644\u06cc \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u0642\u0627\u0628\u0644 \u062a\u0641\u06a9\u06cc\u06a9 \u0627\u0633\u062a \u0648 \u0636\u0631\u0627\u06cc\u0628 \u0628\u062f\u0648\u0646 \u062f\u0633\u062a \u062e\u0648\u0631\u062f\u06af\u06cc \u0627\u0632 \u0636\u0631\u0628 \u062f\u0627\u062e\u0644\u06cc \u062e\u0627\u0631\u062c \u0645\u06cc \u0634\u0648\u0646\u062f:<\/li>\n<\/ul>\n<p><strong>(3)<\/strong><\/p>\n<p dir=\"ltr\" style=\"text-align: center;\">$\\large \\langle \\phi | a\\psi+b\\chi \\rangle = a\\langle \\phi | \\psi \\rangle + b\\langle \\phi | \\chi \\rangle$<\/p>\n<ul>\n<li>\u0636\u0631\u0628 \u062f\u0627\u062e\u0644\u06cc \u0646\u0633\u0628\u062a \u0628\u0647 \u0639\u0627\u0645\u0644 \u0627\u0648\u0644 \u067e\u0627\u062f\u062e\u0637\u06cc \u0627\u0633\u062a\u061b \u06cc\u0639\u0646\u06cc \u0636\u0631\u0628 \u062f\u0627\u062e\u0644\u06cc \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u0642\u0627\u0628\u0644 \u062a\u0641\u06a9\u06cc\u06a9 \u0627\u0633\u062a \u0648 \u0645\u0632\u062f\u0648\u062c \u0645\u062e\u062a\u0644\u0637 \u0636\u0631\u0627\u06cc\u0628 \u0627\u0632 \u0636\u0631\u0628 \u062f\u0627\u062e\u0644\u06cc \u062e\u0627\u0631\u062c \u0645\u06cc \u0634\u0648\u062f:<\/li>\n<\/ul>\n<p><strong>(4)<\/strong><\/p>\n<p dir=\"ltr\" style=\"text-align: center;\">$\\large \\langle a\\psi+b\\chi | \\phi \\rangle = a^*\\langle \\psi | \\phi \\rangle + b^*\\langle \\chi | \\phi \\rangle$<\/p>\n<ul>\n<li>\u0636\u0631\u0628 \u062f\u0627\u062e\u0644\u06cc \u0628\u0631\u062f\u0627\u0631 \u062f\u0631 \u062e\u0648\u062f\u0634 \u0647\u0645\u0648\u0627\u0631\u0647 \u0646\u0627\u0645\u0646\u0641\u06cc \u0627\u0633\u062a (\u062a\u0646\u0647\u0627 \u062f\u0631 \u0635\u0648\u0631\u062a\u06cc \u0635\u0641\u0631 \u0627\u0633\u062a \u06a9\u0647 \u0628\u0631\u062f\u0627\u0631 \u0635\u0641\u0631 \u0628\u0627\u0634\u062f). \u0628\u0647 \u0631\u0627\u062f\u06cc\u06a9\u0627\u0644 \u062d\u0627\u0635\u0644 \u0627\u06cc\u0646 \u0636\u0631\u0628\u060c<strong> \u0646\u0631\u0645 \u0628\u0631\u062f\u0627\u0631<\/strong> \u0645\u06cc \u06af\u0648\u06cc\u06cc\u0645. \u0628\u0631\u0627\u06cc \u0628\u0631\u062f\u0627\u0631 $\\psi$ \u0646\u0631\u0645 \u0622\u0646 \u0631\u0627 \u0628\u0627 \u0639\u0644\u0627\u0645\u062a $||\\psi||$ \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u06cc\u0645.<\/li>\n<\/ul>\n<p><strong>(5)<\/strong><\/p>\n<p dir=\"ltr\" style=\"text-align: center;\">$\\large \\langle \\psi | \\psi \\rangle = || \\psi ||^2 \\geq 0$<\/p>\n<ul>\n<li>\u0641\u0636\u0627\u06cc \u0647\u06cc\u0644\u0628\u0631\u062a \u06a9\u0627\u0645\u0644 \u0627\u0633\u062a. \u0647\u0631 \u062f\u0646\u0628\u0627\u0644\u0647 \u06a9\u0648\u0634\u06cc \u0627\u0632 \u0639\u0646\u0627\u0635\u0631 \u0628\u0631\u062f\u0627\u0631\u06cc $\\mathcal{H}$ \u0628\u0647 \u06cc\u06a9 \u0639\u0646\u0635\u0631 \u0628\u0631\u062f\u0627\u0631\u06cc $\\mathcal{H}$ \u062f\u0631 \u0647\u0645\u0627\u0646 \u0641\u0636\u0627 \u0647\u0645\u06af\u0631\u0627 \u0645\u06cc \u0634\u0648\u062f. \u0628\u0647 \u0628\u06cc\u0627\u0646 \u0633\u0627\u062f\u0647 \u0647\u06cc\u0686 \u062d\u0641\u0631\u0647 \u0627\u06cc \u062f\u0631 \u0641\u0636\u0627\u06cc \u0647\u06cc\u0644\u0628\u0631\u062a \u0646\u06cc\u0633\u062a(\u0647\u0645\u0627\u0646\u0646\u062f \u0645\u062c\u0645\u0648\u0639\u0647 \u0627\u0639\u062f\u0627\u062f \u062d\u0642\u06cc\u0642\u06cc \u06a9\u0647 \u062d\u0641\u0631\u0647 \u0627\u06cc \u0646\u062f\u0627\u0631\u062f \u0627\u0645\u0627 \u0645\u062c\u0645\u0648\u0639\u0647 \u0627\u0639\u062f\u0627\u062f \u06af\u0648\u06cc\u0627 \u062f\u0627\u0631\u0627\u06cc \u062d\u0641\u0631\u0647 \u0647\u0627\u06cc\u06cc \u0627\u0633\u062a).<\/li>\n<\/ul>\n<h5>**\u0645\u062b\u0627\u0644 1-1) \u0646\u0627\u0645\u0633\u0627\u0648\u06cc \u0634\u0648\u0627\u0631\u062a\u0632<\/h5>\n<p>\u0628\u0627 \u0641\u0631\u0636 \u06af\u0631\u0641\u062a\u0646 \u0631\u0627\u0628\u0637\u0647 (5)\u060c \u062b\u0627\u0628\u062a \u06a9\u0646\u06cc\u062f \u0628\u0631\u0627\u06cc \u062f\u0648 \u0628\u0631\u062f\u0627\u0631 $\\psi$ \u0648 $\\phi$ \u062f\u0631 \u0641\u0636\u0627\u06cc $\\mathcal{H}$ \u0646\u0627\u0645\u0633\u0627\u0648\u06cc \u0634\u0648\u0627\u0631\u062a\u0632 \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u0628\u0631\u0642\u0631\u0627\u0631 \u0627\u0633\u062a:<\/p>\n<p><strong>(6)<\/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<h5>\u067e\u0627\u0633\u062e<\/h5>\n<p>\u0627\u062b\u0628\u0627\u062a \u0646\u0627\u0645\u0633\u0627\u0648\u06cc \u0634\u0648\u0627\u0631\u062a\u0632 \u062e\u0644\u0627\u0642\u0627\u0646\u0647 \u0627\u0633\u062a. \u0628\u0627 \u0641\u0631\u0636 \u0627\u06cc\u0646\u06a9\u0647 $a$ \u06cc\u06a9 \u0639\u062f\u062f \u0645\u062e\u062a\u0644\u0637 \u0627\u0633\u062a\u061b \u0627\u0632 \u0631\u0627\u0628\u0637\u0647 (5) \u0648 \u0627\u06cc\u0646\u06a9\u0647 \u062a\u0631\u06a9\u06cc\u0628 \u062e\u0637\u06cc $\\psi$ \u0648 $\\phi$ \u0646\u06cc\u0632 \u062f\u0631 \u0641\u0636\u0627\u06cc \u0647\u06cc\u0644\u0628\u0631\u062a \u0627\u0633\u062a\u060c \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645:<\/p>\n<p dir=\"ltr\">$\\large \\langle \\psi-a\\phi|\\psi-a\\phi\\rangle \\geq 0$<\/p>\n<p>\u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0631\u0627\u0628\u0637\u0647 (3) \u0648 (4)\u060c \u0633\u0645\u062a \u0686\u067e \u0646\u0627\u0645\u0633\u0627\u0648\u06cc \u0631\u0627 \u0628\u0627\u0632 \u0645\u06cc \u06a9\u0646\u06cc\u0645:<\/p>\n<p dir=\"ltr\">$\\large \\langle \\psi-a\\phi|\\psi\\rangle -a\\langle \\psi-a\\phi|\\phi \\rangle \\geq 0$<\/p>\n<p><strong>(7)<\/strong><\/p>\n<p dir=\"ltr\">$\\large \\langle \\psi | \\psi \\rangle &#8211; a^{*}\\langle \\phi | \\psi\\rangle &#8211; a \\langle \\psi| \\phi\\rangle +a^* a \\langle \\phi|\\phi \\rangle \\geq 0$<\/p>\n<p>\u0628\u062f\u0648\u0646 \u0627\u0632 \u0628\u06cc\u0646 \u0631\u0641\u062a\u0646 \u06a9\u0644\u06cc\u062a \u0645\u0633\u0626\u0644\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0627\u0632 \u0639\u0628\u0627\u0631\u062a \u0633\u0645\u062a \u0686\u067e \u0646\u0627\u0645\u0633\u0627\u0648\u06cc \u0646\u0633\u0628\u062a \u0628\u0647 $a^*$ \u0645\u0634\u062a\u0642 \u062c\u0632\u0626\u06cc \u0628\u06af\u06cc\u0631\u06cc\u0645 \u062a\u0627 \u062d\u062f\u0627\u0642\u0644 \u0645\u0642\u062f\u0627\u0631 $a$ \u06a9\u0647 \u0631\u0627\u0628\u0637\u0647 \u0628\u0627\u0644\u0627 \u0631\u0627 \u0628\u0631\u0642\u0631\u0627\u0631 \u06a9\u0646\u062f \u0645\u062d\u0627\u0633\u0628\u0647 \u06a9\u0646\u06cc\u0645:<\/p>\n<p dir=\"ltr\">$\\large &#8211; \\langle \\phi | \\psi\\rangle + a \\langle \\phi|\\phi \\rangle=0 \\Rightarrow a=\\displaystyle{\\frac{\\langle \\phi | \\psi\\rangle}{\\langle \\phi|\\phi \\rangle}}$<\/p>\n<p>\u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0627 \u0631\u0627\u0628\u0637\u0647 \u0628\u0627\u0644\u0627 \u0648 \u0631\u0627\u0628\u0637\u0647 (2)\u060c \u0645\u06cc \u062a\u0648\u0627\u0646 $a^*$ \u0631\u0627 \u0628\u062f\u0633\u062a \u0622\u0648\u0631\u062f (\u06a9\u0627\u0641\u06cc \u0627\u0633\u062a \u0627\u0632 \u0635\u0648\u0631\u062a \u0648 \u0645\u062e\u0631\u062c $a$ \u0645\u0632\u062f\u0648\u062c \u0645\u062e\u062a\u0644\u0637 \u0628\u06af\u06cc\u0631\u06cc\u0645):<\/p>\n<p dir=\"ltr\">$\\large a^*=\\displaystyle{\\frac{\\langle \\psi | \\phi\\rangle}{\\langle \\phi|\\phi \\rangle}}$<\/p>\n<p>\u062d\u0627\u0644 $a$ \u0648 $a^*$ \u0628\u062f\u0633\u062a \u0622\u0645\u062f\u0647 \u0631\u0627 \u062f\u0631 \u0631\u0627\u0628\u0637\u0647 (7) \u062c\u0627\u06cc\u06af\u0630\u0627\u0631\u06cc \u0645\u06cc \u06a9\u0646\u06cc\u0645:<\/p>\n<p dir=\"ltr\">$\\large \\langle \\psi | \\psi \\rangle &#8211; \\frac{\\langle \\psi | \\phi\\rangle \\langle \\phi | \\psi\\rangle}{\\langle \\phi | \\phi\\rangle} \\geq 0 $<\/p>\n<p>\u0628\u0647 \u0633\u0627\u062f\u06af\u06cc \u0627\u0632 \u0631\u0627\u0628\u0637\u0647 \u0628\u0627\u0644\u0627\u060c \u0646\u0627\u0645\u0633\u0627\u0648\u06cc \u0634\u0648\u0627\u0631\u062a\u0632 \u0646\u062a\u06cc\u062c\u0647 \u0645\u06cc \u0634\u0648\u062f.<\/p>\n<p dir=\"ltr\">$\\large | \\langle \\psi | \\phi\\rangle |^2 \\leq \\langle \\psi | \\psi \\rangle \\langle \\phi | \\phi \\rangle$<\/p>\n<hr \/>\n<h3>3-1 \u062c\u0645\u0639 \u0628\u0646\u062f\u06cc \u0641\u0635\u0644<\/h3>\n<p>\u0628\u0627 \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u0641\u0636\u0627\u06cc \u0647\u06cc\u0644\u0628\u0631\u062a\u060c \u0641\u0636\u0627\u06cc\u06cc \u06a9\u0647 \u062a\u0648\u0627\u0628\u0639 \u0645\u0648\u062c \u06a9\u0648\u0627\u0646\u062a\u0648\u0645\u06cc \u062f\u0631 \u0622\u0646 \u0632\u0646\u062f\u06af\u06cc \u0645\u06cc \u06a9\u0646\u0646\u062f\u060c \u0622\u0634\u0646\u0627 \u0634\u062f\u06cc\u0645. \u0627\u06cc\u0646 \u0631\u0627 \u062f\u0631\u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u062f \u06a9\u0647 \u0628\u0631\u062f\u0627\u0631\u0647\u0627\u06cc \u0645\u06a9\u0627\u0646\u06cc\u06a9 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645\u06cc\u060c \u062f\u0631 \u0627\u063a\u0644\u0628 \u0645\u0633\u0627\u0626\u0644 \u062a\u0648\u0627\u0628\u0639\u06cc \u0647\u0633\u062a\u0646\u062f \u06a9\u0647 \u062f\u0631 \u0641\u0636\u0627\u06cc \u0646\u0627\u0645\u062a\u0646\u0627\u0647\u06cc \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u0646\u062f. \u062f\u0631 \u0641\u0635\u0648\u0644 \u0622\u06cc\u0646\u062f\u0647 \u0628\u0627 \u0627\u06cc\u0646 \u062a\u0648\u0627\u0628\u0639 \u0628\u06cc\u0634\u062a\u0631 \u0622\u0634\u0646\u0627 \u0645\u06cc \u0634\u0648\u06cc\u0645.<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u062f\u0631 \u0633\u0644\u0633\u0644\u0647 \u0641\u0635\u0644 \u0647\u0627\u06cc\u06cc \u0628\u0647 \u0645\u0641\u0627\u0647\u06cc\u0645 \u0648 \u0645\u0637\u0627\u0644\u0628 \u0645\u06a9\u0627\u0646\u06cc\u06a9 \u06a9\u0648\u0627\u0646\u062a\u0648\u0645 \u0645\u06cc \u067e\u0631\u062f\u0627\u0632\u0645. \u0628\u0631\u0627\u06cc \u0627\u06cc\u0646\u06a9\u0647 \u062f\u0633\u062a\u06cc\u0627\u0628\u06cc \u0628\u0647 \u0645\u0637\u0627\u0644\u0628 \u0633\u0627\u062f\u0647 \u062a\u0631 \u0628\u0627\u0634\u062f\u061b \u0641\u0635\u0644 \u0647\u0627 \u06a9\u0648\u062a\u0627\u0647 \u062a\u0631\u0646\u062f \u062a\u0627 \u0639\u0646\u0627\u0648\u06cc\u0646 \u0645\u062a\u0645\u0627\u06cc\u0632 \u0648 \u062f\u0631 \u062f\u0633\u062a\u0631\u0633 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