or a simple harmonic oscillator potential, Vo(x) = ÷kx² = ¬mo²x², %3D %3D 2 ħo and the ground state 2 e ground state energy eigenvalue is E igenfunction is a?x? то exp where a? %3D 2
or a simple harmonic oscillator potential, Vo(x) = ÷kx² = ¬mo²x², %3D %3D 2 ħo and the ground state 2 e ground state energy eigenvalue is E igenfunction is a?x? то exp where a? %3D 2
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For a simple harmonic oscillator potential, Vo(x) =kx² = mo'x?,
%|
2
ħo
and the ground state
2
the ground state energy eigenvalue is E
eigenfunction is
a²x?
то
exp
where a?
%3D
2
Now suppose that the potential has a small perturbation,
1
kx² →
1
-kx? + λxό.
2
Vo(x):
→ V(x) =
Use perturbation theory to find the (first order) corrected eigenvalue, in terms of @.
[7]
1x 3 x 5 x ...× (2n – 1)
2n+1Bn
You will need:
x2" exp(-ßx²) dx =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F54b86472-38a1-475d-8e60-9b6db853d5a2%2F3288d69b-c383-48ea-b8ad-6e52ee17a1a7%2Fsdhap4_processed.png&w=3840&q=75)
Transcribed Image Text:1
1
For a simple harmonic oscillator potential, Vo(x) =kx² = mo'x?,
%|
2
ħo
and the ground state
2
the ground state energy eigenvalue is E
eigenfunction is
a²x?
то
exp
where a?
%3D
2
Now suppose that the potential has a small perturbation,
1
kx² →
1
-kx? + λxό.
2
Vo(x):
→ V(x) =
Use perturbation theory to find the (first order) corrected eigenvalue, in terms of @.
[7]
1x 3 x 5 x ...× (2n – 1)
2n+1Bn
You will need:
x2" exp(-ßx²) dx =
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