2) ( Consider an electron trapped in a one-dimensional anharmonic potential. The Hamiltonian for this system is given as: ÂĤ = P²4 mw²g² degenerate perturbation theory by letting the perturbation be: A, = Bx³. + 2m + B23 . Regarding the cubic term as being small, apply non- 2 а) Calculate to first order the ground state energy of this anharmonic oscillator. b) ( Calculate to second order the ground state energy of this anharmonic oscillator. c) ( Find the lowest order correction to the ground state wave function.
2) ( Consider an electron trapped in a one-dimensional anharmonic potential. The Hamiltonian for this system is given as: ÂĤ = P²4 mw²g² degenerate perturbation theory by letting the perturbation be: A, = Bx³. + 2m + B23 . Regarding the cubic term as being small, apply non- 2 а) Calculate to first order the ground state energy of this anharmonic oscillator. b) ( Calculate to second order the ground state energy of this anharmonic oscillator. c) ( Find the lowest order correction to the ground state wave function.
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Transcribed Image Text:2) (
Consider an electron trapped in a one-dimensional anharmonic potential. The Hamiltonian for
this system is given as: H
mw?£?
+
2m
+ B&3 . Regarding the cubic term as being small, apply non-
degenerate perturbation theory by letting the perturbation be: A, = ß2³.
а)
Calculate to first order the ground state energy of this anharmonic oscillator.
b) (
| Calculate to second order the ground state energy of this anharmonic oscillator.
c) (
Find the lowest order correction to the ground state wave function.
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