pert - Time Independent, Multi-Level Perturbation Theory...

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Unformatted text preview: Time Independent, Multi-Level Perturbation Theory Given solutions H E n n n ( ) ( ) ( ) ( ) = (1) Find the perturbed energy and wavefunctions. Noting that will be set to 1, the perturbed Hamiltonian and wavefunction are H H H H = + + + ( ) ( ) ( ) ... 1 2 2 (2) n n n n = + + + ( ) ( ) ( ) ... 1 2 2 (3) which has energies E E E E n n n n = + + + ( ) ( ) ( ) ... 1 2 2 (4) the Schroedinger equation is H H H E E E n n n n n n n n n ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ... ... ... ... 1 2 2 1 2 2 1 2 2 1 2 2 + + + + + + = + + + + + + (5) multiplying-out, collecting terms in 1 1 1 1 1 2 2 1 1 2 2 1 1 2 H E H H E E H H H E E E n n n n n n n n n n n n n n n n n n ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ...- + + - - + + + - - - + = n s n s n s (6) since is arbitrary, each power of is zero separately, giving H E n n n ( ) ( ) ( ) = (7) H H E E n n n n n n ( ) ( ) ( ) ( )...
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This note was uploaded on 07/17/2008 for the course CHEM 861 taught by Professor Dr.coe during the Fall '04 term at Ohio State.

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pert - Time Independent, Multi-Level Perturbation Theory...

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