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how to solve?? #5. (Density of states: 15 pts) (a) In a 3-dimensional infinite cubic potential...
4. 3D Infinite Square Well Perturbation (20 pts) Consider the three-dimensional infinite cubic well: otherwise The stationary states are where n, ny, and n, are integers. The corresponding allowed en...
4. 3D Infinite Square Well Perturbation (20 pts) Consider the three-dimensional infinite cubic well: otherwise The stationary states are where n, ny, and n, are integers. The corresponding allowed energies are Now let us introduce the perturbation otherwise a) Find the first-order correction to the ground state energy b) Find the first-order correction to the first excited state
4. 3D Infinite Square Well Perturbation (20 pts) Consider the three-dimensional infinite cubic well: otherwise The stationary states are where n, ny,...
Solve Schrodinger's equation and derive the wavefunction solution for a 1-dimensional infinite potential well centered between...
Solve Schrodinger's equation and derive the wavefunction solution for a 1-dimensional infinite potential well centered between -a/2 < x < a/2. Plot the wavefunction for the n=1,2, and 3 states. Please help me by showing all the steps.
1. Solve Schrodinger's equation and derive the wavefunction solution for a 1-dimensional infinite potential well centered...
1. Solve Schrodinger's equation and derive the wavefunction solution for a 1-dimensional infinite potential well centered between -L/2 < x < L/2. 2. Find the normalized wavefunction for the solutions found in question 1. Please show all work. Thanks in advance.
(15 points) Encounter with a semi-infinite potential "well" In this problem we will investigate one situation involving a a semi-infinite one-dimensional po- tential well (Figure 1) U=0 regio...
(15 points) Encounter with a semi-infinite potential "well" In this problem we will investigate one situation involving a a semi-infinite one-dimensional po- tential well (Figure 1) U=0 region 1 region 2 region 3 Figure 1: Semi-infinite potential for Problem 3 This potential is piecewise defined as follows where Uo is some positive value of energy. The three intervals in x have been labeled region 1,2 and 3 in Figure 1 Consider a particle of mass m f 0 moving in...
The one-dimensional infinite potential well can be generalized to three dimensions.
(25 marks) The one-dimensional infinite potential well can be generalized to three dimensions. The allowed energies for a particle of mass \(m\) in a cubic box of side \(L\) are given by$$ E_{n_{p} n_{r, n_{i}}}=\frac{\pi^{2} \hbar^{2}}{2 m L^{2}}\left(n_{x}^{2}+n_{y}^{2}+n_{z}^{2}\right) \quad\left(n_{x}=1,2, \ldots ; n_{y}=1,2, \ldots ; n_{z}=1,2, \ldots\right) $$(a) If we put four electrons inside the box, what is the ground-state energy of the system? Here the ground-state energy is defined to be the minimum energy of the system of electrons. You...
A NON stationary state A particle of mass m is in an infinite square well potential of width L, a...
A NON stationary state A particle of mass m is in an infinite square well potential of width L, as in McIntyre's section 5.4. Suppose we have an initial state vector lv(t -0) results from Mclntrye without re-deriving them, and you may use a computer for your math as long as you include your code in your solution A(3E1) 4iE2)). You may use E. (4 pts) Use a computer to plot this probability density at 4 times: t 0, t2...
5. One-Dimensional Potential Energy (20 points) A particle of mass m oscillates in a potential well...
5. One-Dimensional Potential Energy (20 points) A particle of mass m oscillates in a potential well created by a one-dimensional force where a and b are known positive constants. Assume the particle is trapped in the well on the positive side of the y-axis. a) Find and expression for the potential energy U(x) for this force. (10 points) NOTE: There will be one undetermined constant. b) Set Umin, the minimum value for this potential energy function, equal to zero. Solve...
Find parts a and b. Consider the three-dimensional cubic well V = {(0 if 0<x<a, 0<y<a,...
Find parts a and b.
Consider the three-dimensional cubic well V = {(0 if
0<x<a, 0<y<a, 0<z<a), (infinity otherwise).
The stationary states are psi^(0) (x, Y, z) =
(2/a)^(3/2)sin(npix/a)sin(npiy/a) sin(npiz/a), where nx, ny , and
nz are integers.
The corresponding allowed energies are E^0 =
(((pi^2)(hbar^2))/2m(a^2))(nx^2+ny^2+nz^2).
Now let us introduce perturbation V={(V0 if
0<x<(a/2), 0<y<(a/2)), (0 otherwise)
a) Find the first-order correction to the ground state
energy.
b) Find the first-order correction to the first
excited state.
1. Consider the...
1l] A particle with mass m and energy E is inside a square tube with infinite potential barriers at x-o, x-a, y 0,...
1l] A particle with mass m and energy E is inside a square tube with infinite potential barriers at x-o, x-a, y 0, y a. The tube is infinitely long in the +z-direction. (a) Solve the Schroedinger equation to derive the allowed wave functions for this particle. Do not try to normalize the wave functions, but make sure they correspond to motion in +2-direction. (b) Determine the allowed energies for such a particle. (c) If we were to probe the...
(15 pts) Given the 5-point signal space diagram shown below, can you find an alter- native 2-dimensional signal set with the same number of signals, lower average energy and a lower probability of sy...
(15 pts) Given the 5-point signal space diagram shown below, can you find an alter- native 2-dimensional signal set with the same number of signals, lower average energy and a lower probability of symbol error at high SNR? Assume signals are equally likely. Draw and label your signals very neatly. Justify your answer 3 3 -21 -1 -2 -3
(15 pts) Given the 5-point signal space diagram shown below, can you find an alter- native 2-dimensional signal set with the...
4. 3D Infinite Square Well Perturbation (20 pts) Consider the three-dimensional infinite cubic well: otherwise The stationary states are where n, ny, and n, are integers. The corresponding allowed energies are Now let us introduce the perturbation otherwise a) Find the first-order correction to the ground state energy b) Find the first-order correction to the first excited state
4. 3D Infinite Square Well Perturbation (20 pts) Consider the three-dimensional infinite cubic well: otherwise The stationary states are where n, ny,...
(15 points) Encounter with a semi-infinite potential "well" In this problem we will investigate one situation involving a a semi-infinite one-dimensional po- tential well (Figure 1) U=0 region 1 region 2 region 3 Figure 1: Semi-infinite potential for Problem 3 This potential is piecewise defined as follows where Uo is some positive value of energy. The three intervals in x have been labeled region 1,2 and 3 in Figure 1 Consider a particle of mass m f 0 moving in...
A NON stationary state A particle of mass m is in an infinite square well potential of width L, as in McIntyre's section 5.4. Suppose we have an initial state vector lv(t -0) results from Mclntrye without re-deriving them, and you may use a computer for your math as long as you include your code in your solution A(3E1) 4iE2)). You may use E. (4 pts) Use a computer to plot this probability density at 4 times: t 0, t2...
5. One-Dimensional Potential Energy (20 points) A particle of mass m oscillates in a potential well created by a one-dimensional force where a and b are known positive constants. Assume the particle is trapped in the well on the positive side of the y-axis. a) Find and expression for the potential energy U(x) for this force. (10 points) NOTE: There will be one undetermined constant. b) Set Umin, the minimum value for this potential energy function, equal to zero. Solve...
Find parts a and b.
Consider the three-dimensional cubic well V = {(0 if
0<x<a, 0<y<a, 0<z<a), (infinity otherwise).
The stationary states are psi^(0) (x, Y, z) =
(2/a)^(3/2)sin(npix/a)sin(npiy/a) sin(npiz/a), where nx, ny , and
nz are integers.
The corresponding allowed energies are E^0 =
(((pi^2)(hbar^2))/2m(a^2))(nx^2+ny^2+nz^2).
Now let us introduce perturbation V={(V0 if
0<x<(a/2), 0<y<(a/2)), (0 otherwise)
a) Find the first-order correction to the ground state
energy.
b) Find the first-order correction to the first
excited state.
1. Consider the...
1l] A particle with mass m and energy E is inside a square tube with infinite potential barriers at x-o, x-a, y 0, y a. The tube is infinitely long in the +z-direction. (a) Solve the Schroedinger equation to derive the allowed wave functions for this particle. Do not try to normalize the wave functions, but make sure they correspond to motion in +2-direction. (b) Determine the allowed energies for such a particle. (c) If we were to probe the...
(15 pts) Given the 5-point signal space diagram shown below, can you find an alter- native 2-dimensional signal set with the same number of signals, lower average energy and a lower probability of symbol error at high SNR? Assume signals are equally likely. Draw and label your signals very neatly. Justify your answer 3 3 -21 -1 -2 -3
(15 pts) Given the 5-point signal space diagram shown below, can you find an alter- native 2-dimensional signal set with the...
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