Question 5 5.1 A one-dimension harmonic oscillator of charge q is perturbed by the application of an electric field E in the x direction, making the potential energy V(x) = mw²: w ²-qEx. (i) Show that the first-order perturbation in each energy level is zero. (ii) Show that the second order perturbation in the in energy of the lowest (n = 0) level is - 9²E² 2mw2¹ [Given: n(x) = A" exp(-x²) where A is an operator and a = mw/h]. (1) E¹) - En = Vnn = Vn v(x) ndx E(2)=E(1¹) + Esen) |vsn|² En-Es 5.2 A particle of mass m is subjected to the spherically symmetric attractive square well potential defined by -Vo V(r) = ) = {6," 0 a Derive the equations needed to find the bound states of zero angular momentum.
Question 5 5.1 A one-dimension harmonic oscillator of charge q is perturbed by the application of an electric field E in the x direction, making the potential energy V(x) = mw²: w ²-qEx. (i) Show that the first-order perturbation in each energy level is zero. (ii) Show that the second order perturbation in the in energy of the lowest (n = 0) level is - 9²E² 2mw2¹ [Given: n(x) = A" exp(-x²) where A is an operator and a = mw/h]. (1) E¹) - En = Vnn = Vn v(x) ndx E(2)=E(1¹) + Esen) |vsn|² En-Es 5.2 A particle of mass m is subjected to the spherically symmetric attractive square well potential defined by -Vo V(r) = ) = {6," 0 a Derive the equations needed to find the bound states of zero angular momentum.
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![Question 5
5.1 A one-dimension harmonic oscillator of charge q is perturbed by the application of an
electric field E in the x direction, making the potential energy
V(x) = mw²:
w ²-qEx.
Show that the first-order perturbation in each energy level is zero.
Show that the second order perturbation in the in energy of the lowest (n = 0)
9²E²
level is -
2mw2¹
[Given: n(x) = A" exp(-x²)
where A is an operator and a = mw/h].
(1)
E¹) - En = Vnn = Vn v(x) ndx
E(2) = E(¹) + Esen]
|vsn|²
En-Es
5.2
A particle of mass m is subjected to the spherically symmetric attractive square well potential
defined by
-Vo
V(r) =
) = {6,"
0<r <a
r> a
Derive the equations needed to find the bound states of zero angular momentum.
(i)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0eefe4ae-189e-40e6-80d8-7922abba3e32%2F3a3246c1-4185-467f-a9a5-b181b3301f6d%2F9tfgp62_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 5
5.1 A one-dimension harmonic oscillator of charge q is perturbed by the application of an
electric field E in the x direction, making the potential energy
V(x) = mw²:
w ²-qEx.
Show that the first-order perturbation in each energy level is zero.
Show that the second order perturbation in the in energy of the lowest (n = 0)
9²E²
level is -
2mw2¹
[Given: n(x) = A" exp(-x²)
where A is an operator and a = mw/h].
(1)
E¹) - En = Vnn = Vn v(x) ndx
E(2) = E(¹) + Esen]
|vsn|²
En-Es
5.2
A particle of mass m is subjected to the spherically symmetric attractive square well potential
defined by
-Vo
V(r) =
) = {6,"
0<r <a
r> a
Derive the equations needed to find the bound states of zero angular momentum.
(i)
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