Calculate the energy of the nth excited state to second-order perturbation and the wave function 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: (b) Vp(x) = { ¯ Vo(1-x²/1²), \x|
Calculate the energy of the nth excited state to second-order perturbation and the wave function 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: (b) Vp(x) = { ¯ Vo(1-x²/1²), \x|
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2. 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 9.3
Calculate the energy of the nth excited state to second-order perturbation and the wave function
to first-order perturbation for a one-dimensional box potential of length 2L, with walls at x =
-L and x = I, which is modified at the bottom by the following perturbations with Vo <<< 1:
-L≤x≤ 0,
0≤x≤ L;
(b) Vp(x) = { - Vo(1-x²/1²), [x] <I,
0,
elsewhere.
(a) Vp(x) = {
0,
Vo,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F72961f9b-daa2-4465-be98-f8e609ec1d69%2Feedcb417-b2bc-43f4-88a6-56606da15ee3%2F92rgxr8_processed.png&w=3840&q=75)
Transcribed Image Text:Exercise 9.3
Calculate the energy of the nth excited state to second-order perturbation and the wave function
to first-order perturbation for a one-dimensional box potential of length 2L, with walls at x =
-L and x = I, which is modified at the bottom by the following perturbations with Vo <<< 1:
-L≤x≤ 0,
0≤x≤ L;
(b) Vp(x) = { - Vo(1-x²/1²), [x] <I,
0,
elsewhere.
(a) Vp(x) = {
0,
Vo,
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