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--- classes:2009:fall:phys4101.001:lec_notes_1116 [2009/11/19 08:54] – yk
+++ classes:2009:fall:phys4101.001:lec_notes_1116 [2009/11/19 11:59] (current) – yk
@@ Line 1: / Line 1: @@
-===== Nov 16 (Mon)  =====
+===== Nov 16 (Mon) Angular momentum with raising/lowing operators =====
 ** Responsible party: Pluto 4ever, malmx026  **
@@ Line 24: / Line 24: @@
 ^ ^ SHO ^ Angluar momentum ^
-|The hamiltonian, H,  is proportional to | <math>x^2 + p^2</math>|<math>{L_x}^2 + {L_y}^2</math>|
+|The hamiltonian, H,  is proportional to | <math>x^2 + p^2</math>|<math>{L_x}^2 + {L_y}^2(+L^2_z)</math>|
-|We tried to factorize H by |<math>(x+ip)(x-ip)</math> | <math>(L_x+iL_y)(L_x-iL_y)</math> |
+|We tried to factorize H by |<math>(x+ip)(x-ip)</math> | <math>(L_x+iL_y)(L_x-iL_y) (+L^2_z)</math> |
 |Call these terms| <math>a_\pm\approx \mp ip + x</math> |<math>L_\pm\approx \pm iL_y + L_x</math> |
 |factorization is not perfect so H is|<math>a_+a_-+1/2</math>|<math>L_+L_-+\hbar L_z (+L^2_z)</math>|