lecture_3tuckerman quantum mechanics

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tuckerman quantum mechanics

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Page 1: lecture_3tuckerman quantum mechanics

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¸ � � � � ° � � µ¸ � � ° ��� µ § � © ¸ � � ° � � µ¸ � � ° ��� µ ¡½�"©~�t7]�_C]>dei^_T]^�xy�]Ht�gk[^] ¥ �{� �J� �O ¥ �{� �O  § � ©¾ o�lvb"g|fvb�i�� f�]�g^_OoCtcg|o�]���acg|f�lno�`º�>g^q�irq7f�`�t7i^fvu�l£d ° ©{¡½¿Hg^qcu ° ��¡ » �7ÀzÁ » �+l�q�y"t7lv��t���g^bC]^�� �O E¡$� ��©� ~�t7]H� irqc� f�acbClnirq�lvbOoCtcg|o"��©{lvb��xoCt7]�_C]>dei^_T]^�+g�f�ipyO]>_O��ira7qcu�i^q�oTt7]Mi^q ¥ �s  �+y"t7l���t�mR]�g^qcb�oCtcg|o�yO]M�>g|q�g|h7hc_Cikj+l�mRg|oC]{�"©M��`�gmRlnqclnmRl���gpoTlnirq�i|d ¥ �s Oy"lnoCt�_C]�b�h5]�� o"oCi�g|qx`�h�g|_�g|mR] oT]>_�b«oTtcgpo� �O OmRl��^t�o�u+]>h5]>q�u�i^q�}

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¥ �s �¡·Ë¢ÌrÍ � ³ Æ Í Ê����{Æ Í ÊË Ì^Í � ³ Æ Í Ê��EÆ Í Êy"t7lv��t¼bCt7ipy�boCtcg|o ¥ �s �u+]>h5]>q�u7bRi^qWg|f�fO[pg^fna7]�b�i|d�oTt7]�dea7qc�UoTlnirq¼�{Æ Í ÊU�«y"tcl���tWl�b�wxq7ipy"qWg^b�gJÎ�ÏUÐÇÃpÄ"Ñ«Ã|ÒkÓHÔ�Õ+ÖØ× Î�ÐÇÙpÖ�}J¬z]^�oCtc]>_T] dei^_T]^�Y�>g^fnf ¥ �s Hg�Ô�Õ+Ö5×>Î�ÐÇÙpÖ5Ã|Ä@i|d��EÆ Í ÊU}�Ú�ixi�b�]�fn`sbCh5]�g|wxl�q7�c��g�dea7qc�UoTlnirqcg|f«l�bgºdeacqc�UoTlnirq/i|d"g�dea7qc�UoTlnirq�}º¬z]^��oCtc]>_T] dei^_T]^�u+]�q7i|oT]MoCt7]M[pg|_Tl�g|oCl�i^qcg^fØdea7qc� oCl�i^qcg^f�g^b�ºÛ �«Ü�¡ ¥ �{� �J� �O ¥ �{� �O de_Ti^m�y"t7lv��t�l£o"deirfnf�ipy�b�oCtcg|o ��Û �1Ü § �"©��Û ��© ÜØ¡Ý�"©~�t7]Mdea7qc� oCl�i^qcg^f���tcg^_Tgr�UoC]�_�i|d)��Û �«ÜY��g|q���]�acb�]�u�oCi�u+]�_Cl�[^]Hg|qci|oCtc]>_�l�mRh�ir_�o�g|q�o�h7_Ti^h5]>_Co�`�i|dYoCt7]dea7qc�UoTlnirqcg|f��7y"t7lv��t�lvb�oCt7]b�oTgpoTlnirqcg|_Tlno�`ºh7_Ti^h5]>_Co�`�g^_Cira7qcu�g|qx`�]>l��^]>q�b�o�gpoC]�i|d1�/} ¾ q�ir_Tu+]�_"oCi�u+]>_Tl�[^]MoCtc]b�oTgpoTlnirqcg|_Tlno�`�� irqcu+lnoCl�i^q���y�]�� irqcb�lvu+]�_�m�g|wxlnqc�gRb�m�g^fnf@[pg|_TlvgpoCl�i^q�i|d�oCt7]MoT_Clvg|f-w^] o�gr�>� ir_Tu7lnq7�oCi � �� OÞ5ßà� �O -á'� ¶ �� ¥ �{�+Þ5ß ¥ �M��á ¥ ¶ �M�g|q�uºyO]H]>[pg|f�acg|oC]{oCt7]Mdeacqc�UoTlnirqcg|f-�ºÛ ��á ¶ �1Ü�­

��Û �/á ¶ �1ÜY¡ Û ¥ �{��á ¥ ¶ �M� Ük�\Ûv� �O �á'� ¶ �O �ÜÛ ¥ �M��á ¥ ¶ �M� Ü+Û�� �O �áÝ� ¶ �O ÉÜ ipyH�+yO]My�ir_Cw�oCi�âc_�b�o"i^_�u+]�_"lnq/� ¶ �� �i^_ ¥ ¶ �{�£}«~�txacb>�+yO]M] j+hcg^qcu�oCt7]Mdea7q��UoCl�i^q�g|f�­��Û �Èá ¶ �1ÜY¡½��Û �«Ü7áäã �ã ¥ �{� ¥ ¶ �{�káäã �ã � ��  � ¶ �O YáSå�å>å

g|q�u�oTt7]H_Cl��^t�o�bCl�u+]H�5]��>i^mR]�b¥ �{� ���O -á ¥ ¶ �M� �¼� �� -á ¥ �{� �J� ¶ �O -áSå>å�å¥ �{� �O Yá ¥ �{� ¶ �O -á ¥ ¶ �M� �� -á3å�å>å ¡ ¥ �{� ���O -á ¥ ¶ �M� �¼� �� -á ¥ �{� �J� ¶ �O ¥ �{� �O  æ ¿"Þ ¥ �M� ¶ �� ¥ �M� ��  Þ ¥ ¶ �{� �O ¥ �{� �O �ç¡ ¥ �{� �J� �� ¥ �{� �O  á ¥ ¶ �{� �J� �O ¥ �{� �O  á ¥ �M� �¼� ¶ �� ¥ �M� ��  Þ ¥ �{� �J� �O ¥ �{� �O  ¥ �{� ¶ �O ¥ �{� �O  Þ ¥ �{� �J� �� ¥ �M� ��  ¥ ¶ �{� �O ¥ �{� �O ¡3��Û �1Ü7á ¥ ¶ �{� �J� �O ¥ �{� �O  á ¥ �M� �J� ¶ �O ¥ �M� ��  Þz��Û �1Ü ¥ �M� ¶ �� ¥ �M� ��  ÞÈ��Û �1Ü ¥ ¶ �{� �O ¥ �{� �O ¡3��Û �1Ü7á ¥ ¶ �{� æ �J� �O ¥ �{� �O  Þ ��Û �1Ü�� �� ¥ �M� �� /ç á æ ¥ �{� �¥ �{� �O  Þ ¥ �M� ��Û �1Ü¥ �M� �� /ç � ¶ �� 

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��Æ ��/10 2 Ê"¡ þ� µè(� ���è þ� á �%� µ) è þ��%� ¡ýþ� �è ¡ÿ� ©¾ q�oTt7l�b{�>grb�]r�7oTt7]]>j7g^�UoE�^_Ti^a7qcu�b�oTg|oC]]�q7]>_T�^`�lvb�i^�7oTg|l�q7]�u���]��>g^acb�]�y�]�grbCbCa7mR]�u�oCt7]�� i^_T_T]��Uo"deacqc�UoTlnirqcg|f�dei^_Tm$deir_8oTt7]oT_Clvg|fy�gk[^]Edea7qc�UoTlnirq�}1~�txacb��+oCt7]H�r_Cira7qcu�b�o�gpoC]Hy�gk[^]>dea7qc� oCl�i^qºlvb��>fn]�g|_Tfn`��rln[r]>q���`

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������G�¬�]Hq7ipy'_C]��rg^_Tu�D�g^b"g�[pg|_Tl�g|oCl�i^qcg^fØhcg|_�g|mR] oT]>_�})~�t�a�b>�¥ �{� �O �¡H� �� � Ì^Í ¿Æ Í µ áID µ Ê µ~�t7lvb"l�qroT]>�r_Tg^fØ��g|q���]H]�[pg|f�acgpoT]�u�]�g^bCl�fn`��x`ºg�oT_Cl��^irq7i^mR]>oC_Tl��{b�ac�cb�oTl£oTa+oCl�i^q-­

Í ¡JD1o�g|qLKÌ^Í ¡JD�bC]�� µ Kde_Ti^m�y"t7lv��t¥ �M� �� «¡M�EN 8 µ� N 8 µ

DObC]�� µ K Ì KD : Æ�¿�á/oTg^q µ KrÊ µ¡ ¿D O �EN 8 µ� N 8 µ

�>irb µ K Ì K¡ $è D O¬3lnoCt�gRfnlno�oTfn]g^fn�r]>�7_�g7�xlno8�>g^q��5]b�l�mRlnfvg|_Tf�`ºb�tcipy"qºoTtcgpo¥ �M� �J� �O �¡ $�þ� µ)(� D P áH$ ��� µF D~�txacb�� ¥ �{� �J� �O ¥ �{� �O  ¡ þ� µF � D µ á ¿è �%� µ D µ ¡ÿ�ºÆQD+Ê

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