Calculate the energy of the nth excited state to first-order perturbation for a one-dimensional box potential of length 2L, with walls at x = -L and x = L, which is modified at the bottom by the following perturbations with Vo << 1: I-Vo. -I < x

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Quantum Mechanics Please write the solutions completely (from general formula to derivation of formula) for study purposes. Thank you. Book: Quantum Mechanics Concepts and Applications - Nouredine Zettili
Exercise 9.1
Calculate the energy of the nth excited state to first-order perturbation for a one-dimensional
box potential of length 2L, with walls at x = −L and x = L, which is modified at the bottom
by the following perturbations with Vo << 1:
-1 ≤x≤L,
-Vo₂
0,
(a) Vp(x) = {
(b) Vp(x) = {
-Vo,
0,
elsewhere;
-1/2 ≤ x ≤ 1/2,
elsewhere.
Transcribed Image Text:Exercise 9.1 Calculate the energy of the nth excited state to first-order perturbation for a one-dimensional box potential of length 2L, with walls at x = −L and x = L, which is modified at the bottom by the following perturbations with Vo << 1: -1 ≤x≤L, -Vo₂ 0, (a) Vp(x) = { (b) Vp(x) = { -Vo, 0, elsewhere; -1/2 ≤ x ≤ 1/2, elsewhere.
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