Chem120A+Notes+10-1-08

Chem120A+Notes+10-1-08 - Chem120A Notes 10/1/08 Single...

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Unformatted text preview: Chem120A Notes 10/1/08 Single Particle Subject to Central Force + + = + = + = 2 2 2 2 2 2 2 2 2 ); ( 2 z y x r V m V T H h is called the Laplacian 2 We can also express the Hamiltonian in terms of two components for the kinetic energy: a radial component, and an angular component. ) ( 2 2 2 2 2 2 2 2 r V mr L r r r m H + + + = h , is the angular momentum operator 2 L Particle subject to V(r) has angular momentum conserved. To be able to measure H and L simultaneously, we need [ ] , 2 = L H [ ] [ ] [ ] 2 2 2 , , , L V L T L H + = ( 1 ) [ ] + + + + = 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 , mr L r r r m L L mr L r r r m L T h h Note: is a function of 2 L angles only i.e. ) , ( 2 f L = Therefore, the order of operations for T and dont matter, as T only affects radial portions of the wavefunction, and only affects the radial components i.e. only affects the radial components i....
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Chem120A+Notes+10-1-08 - Chem120A Notes 10/1/08 Single...

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