(e) In the regions where the potential is V₂, the particle's wavefunction satisfies the time- independent Schrödinger equation, which is +ay(x) some constant a₁. What is a in terms of the values given in the problem? d²v(x) dz² = (f) Sketch a possible wavefunction for a quantum particle moving in this potential as a function of x (it doesn't matter which mode, just pick one!). For the oscillating part, make sure to show how the wavelength changes in different regions.
(e) In the regions where the potential is V₂, the particle's wavefunction satisfies the time- independent Schrödinger equation, which is +ay(x) some constant a₁. What is a in terms of the values given in the problem? d²v(x) dz² = (f) Sketch a possible wavefunction for a quantum particle moving in this potential as a function of x (it doesn't matter which mode, just pick one!). For the oscillating part, make sure to show how the wavelength changes in different regions.
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Please answer d,e and f
![A quantum particle of mass m is in the potential given in the figure below. Between x = 0
and x = A the potential is zero and between x = A and x = B the potential is V₁. Outside
this region (if x ≥ B or a ≤ 0), the potential is V₂. Assume the particle has total energy E
which is less than V₂ but greater than V₁, so classically the particle would be trapped between
x = 0 and x = B.
V₂
Energy A
0
V=0
V₁
A
=
V₂
B
X
(a) If this were a classical particle, would it have more kinetic energy (and therefore more
momentum) in the region where the potential is zero or in the region where the potential
is V₁? Explain.
(b) In the region where V = 0, the particle's wavefunction satisfies the time-independent
d²v(x)
Schrödinger equation, which is
-k(r) for some constant k₁. What is k₁ in
dr²
terms of the values given in the problem? What is the corresponding wavelength A₁?
(c) In the region where V = V₁, the particle's wavefunction satisfies the time-independent
Schrödinger equation, which is ²) = -ky(r) for a different constant k₂. What is k₂
in terms of the values given in the problem? What is the corresponding wavelength X₂?
(d) Is A2 larger or smaller than A₁? Is the de Broglie momentum of the particle larger in
the region where the potential is zero or larger where the potential is V₁? How does this
compare to the classical case (part a)?
(e) In the regions where the potential is V₂, the particle's wavefunction satisfies the time-
independent Schrödinger equation, which is d²v(x) = +ay(x) some constant a₁. What
is a₁ in terms of the values given in the problem?
dr²
(f) Sketch a possible wavefunction for a quantum particle moving in this potential as a
function of x (it doesn't matter which mode, just pick one!). For the oscillating part,
make sure to show how the wavelength changes in different regions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe6208a55-bec6-433a-a894-0742aca7c9d7%2F55c54df1-f184-4167-9e26-b91d03733ebd%2Fvpbk68p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A quantum particle of mass m is in the potential given in the figure below. Between x = 0
and x = A the potential is zero and between x = A and x = B the potential is V₁. Outside
this region (if x ≥ B or a ≤ 0), the potential is V₂. Assume the particle has total energy E
which is less than V₂ but greater than V₁, so classically the particle would be trapped between
x = 0 and x = B.
V₂
Energy A
0
V=0
V₁
A
=
V₂
B
X
(a) If this were a classical particle, would it have more kinetic energy (and therefore more
momentum) in the region where the potential is zero or in the region where the potential
is V₁? Explain.
(b) In the region where V = 0, the particle's wavefunction satisfies the time-independent
d²v(x)
Schrödinger equation, which is
-k(r) for some constant k₁. What is k₁ in
dr²
terms of the values given in the problem? What is the corresponding wavelength A₁?
(c) In the region where V = V₁, the particle's wavefunction satisfies the time-independent
Schrödinger equation, which is ²) = -ky(r) for a different constant k₂. What is k₂
in terms of the values given in the problem? What is the corresponding wavelength X₂?
(d) Is A2 larger or smaller than A₁? Is the de Broglie momentum of the particle larger in
the region where the potential is zero or larger where the potential is V₁? How does this
compare to the classical case (part a)?
(e) In the regions where the potential is V₂, the particle's wavefunction satisfies the time-
independent Schrödinger equation, which is d²v(x) = +ay(x) some constant a₁. What
is a₁ in terms of the values given in the problem?
dr²
(f) Sketch a possible wavefunction for a quantum particle moving in this potential as a
function of x (it doesn't matter which mode, just pick one!). For the oscillating part,
make sure to show how the wavelength changes in different regions.
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