Q1) Consider a particle in a one-dimensional infinite well with walls at x=0 and x=a. Suppose a perturbation is applied so that the potential energy is shifted by an amount (x/a)², where E,º = n²h?/(2ma²) is the ground state energy of 10-3E, the unperturbed box. a) Calculate the first order correction to all excited state energies due to the
Q1) Consider a particle in a one-dimensional infinite well with walls at x=0 and x=a. Suppose a perturbation is applied so that the potential energy is shifted by an amount (x/a)², where E,º = n²h?/(2ma²) is the ground state energy of 10-3E, the unperturbed box. a) Calculate the first order correction to all excited state energies due to the
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![Q1) Consider a particle in a one-dimensional infinite well with walls at x=0 and x=a.
Suppose a perturbation is applied so that the potential energy is shifted by an amount
(0)
= n²h?/(2ma²) is the ground state energy
(0)
a H, = 10-3E," (x/a)², where E") of
the unperturbed box.
a) Calculate the first order correction to all excited state energies due to the
perturbation.
b) Calculate the second order correction to all excited state energies due to the perturbation.
(Simplify your result as much as you can, f.eg. taking sin[(k ±n)T] = 0)
c) Calculate the first order correction to the wave function due to the perturbation.
d) Write down the approximate wave function of the perturbed well for the state with
n = 3 corrected up to the 1.st order in perturbation theory . Consider only the first
three non-zero terms in the sum.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F36c9c08b-6c70-43dd-abc6-e25bd3a8b4c8%2Ff20e370b-12d8-4abc-ac43-4ce99fd663c6%2Fpix3xqkz_processed.png&w=3840&q=75)
Transcribed Image Text:Q1) Consider a particle in a one-dimensional infinite well with walls at x=0 and x=a.
Suppose a perturbation is applied so that the potential energy is shifted by an amount
(0)
= n²h?/(2ma²) is the ground state energy
(0)
a H, = 10-3E," (x/a)², where E") of
the unperturbed box.
a) Calculate the first order correction to all excited state energies due to the
perturbation.
b) Calculate the second order correction to all excited state energies due to the perturbation.
(Simplify your result as much as you can, f.eg. taking sin[(k ±n)T] = 0)
c) Calculate the first order correction to the wave function due to the perturbation.
d) Write down the approximate wave function of the perturbed well for the state with
n = 3 corrected up to the 1.st order in perturbation theory . Consider only the first
three non-zero terms in the sum.
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