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hodernl Pllysics 2 due Thursday, April 5 Consider a particle in a 3 dimensional infinite square...
Q1) Consider 2.dimensional infinite "well" with the potential otherwise The stationary states are ny = (a)...
Q1) Consider 2.dimensional infinite "well" with the potential otherwise The stationary states are ny = (a) sin ( x) sin (y,) The corresponding energies are n) , 123 Note that the ground state, ?11 is nondegenerate with the energy E00)-E1)-' r' Now introduce the perturbation, given by the shaded region in the figure ma AH,-{Vo, if 0<x otherwise y<a/2 (a) What is the energy of the 1.st excited state of the unperturbed system? What is its degree of degeneracy,v? (b)...
Part A A three-dimensional potential well has potential Uo = 0 in the region 0 <...
Part A A three-dimensional potential well has potential Uo = 0 in the region 0 < x <L, 0<y<L, and 0 <z<2L and infinite potential otherwise. The ground state energy of a particle in the well is E. What is the energy of the first excited state, and what is the degeneracy of that state? 3Eo, triple degeneracy 2Eo, single degeneracy 2Eo, double degeneracy (7/3)Eo, double degeneracy (4/3)Eo, single degeneracy Submit Request Answer
Consider a particle confined in two-dimensional box with infinite walls at x 0, L;y 0, L. the dou...
quantum mechanics
Consider a particle confined in two-dimensional box with infinite walls at x 0, L;y 0, L. the doubly degenerate eigenstates are: Ιψη, p (x,y))-2sinnLx sinpry for 0 < x, y < L elsewhere and their eigenenergies are: n + p, n, p where n, p-1,2, 3,.... Calculate the energy of the first excited state up to the first order in perturbation theory due to the addition of: 2 2
Consider a particle confined in two-dimensional box with infinite...
4. (20 points) Infinite Wells in Three Dimensions a) Consider a three dimensional in- finite rect...
4. (20 points) Infinite Wells in Three Dimensions a) Consider a three dimensional in- finite rectangular well for which L -L, Ly-2L, ald L2-3L. In terms of quantum numbers (e.g. nz, ny, and n.), M. L, and ћ. write down an expression for the energies of all quantum states. (b) Find the energies of the ground state and the first three lowest lying energies. As in part (b), for each energy level, give the quantum numbers n, ny, n and...
5) A particle of mass m is in the ground state of the infinite square well...
5) A particle of mass m is in the ground state of the infinite square well 0 < x < a At t-0 the right hand wall suddenly moves to x = 2a, doubling the size of the well. Assume that this expansion happens on a time scale so fast that the initial wave function (at t0+) is the same as just before the expansion (at t-0-) (This is called the "sudden" approximation.) a) What is the probability that a...
Consider a particle in a 1-dimensional ininite square well potential {0, V(z)=Í oo, (-a < z...
Consider a particle in a 1-dimensional ininite square well potential {0, V(z)=Í oo, (-a < z <a) elsewhere The particle is initially localized in the right side of the well (O S a) Calculate the probability that at later times, an energy measurement will yield the energy of the first excited state of this system
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,...
An electron (mass m) is trapped ina 2-dimensional infinite square box of sides Lx - L...
An electron (mass m) is trapped ina 2-dimensional infinite square box of sides Lx - L - L. Take Eo = 92/8mL2. Consider the first four energy levels: the ground state and the first three excited states. 1) Calculate the ground-state energy in terms of Ep. (That is, the ground-state energy is what multiple of Eo? Eo Submit 2) In terms of Eo, what is the energy of the first excited state? (That is, the energy of the first excited...
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...
(a) Use the variational method to estimate the ground state energy of a particle of |mass...
(a) Use the variational method to estimate the ground state energy of a particle of |mass m in a potential Vx)kx, k > 0. (b) Calculate the energy shift in the ground state and in the degenerate 1t excited state of a 2-dimensional harmonic oscillator H(P2P,2/2m m(x +y)due to the perturbation V 2Axy. (20 pts)
(a) Use the variational method to estimate the ground state energy of a particle of |mass m in a potential Vx)kx, k > 0. (b)...
Q1) Consider 2.dimensional infinite "well" with the potential otherwise The stationary states are ny = (a) sin ( x) sin (y,) The corresponding energies are n) , 123 Note that the ground state, ?11 is nondegenerate with the energy E00)-E1)-' r' Now introduce the perturbation, given by the shaded region in the figure ma AH,-{Vo, if 0<x otherwise y<a/2 (a) What is the energy of the 1.st excited state of the unperturbed system? What is its degree of degeneracy,v? (b)...
Part A A three-dimensional potential well has potential Uo = 0 in the region 0 < x <L, 0<y<L, and 0 <z<2L and infinite potential otherwise. The ground state energy of a particle in the well is E. What is the energy of the first excited state, and what is the degeneracy of that state? 3Eo, triple degeneracy 2Eo, single degeneracy 2Eo, double degeneracy (7/3)Eo, double degeneracy (4/3)Eo, single degeneracy Submit Request Answer
quantum mechanics
Consider a particle confined in two-dimensional box with infinite walls at x 0, L;y 0, L. the doubly degenerate eigenstates are: Ιψη, p (x,y))-2sinnLx sinpry for 0 < x, y < L elsewhere and their eigenenergies are: n + p, n, p where n, p-1,2, 3,.... Calculate the energy of the first excited state up to the first order in perturbation theory due to the addition of: 2 2
Consider a particle confined in two-dimensional box with infinite...
4. (20 points) Infinite Wells in Three Dimensions a) Consider a three dimensional in- finite rectangular well for which L -L, Ly-2L, ald L2-3L. In terms of quantum numbers (e.g. nz, ny, and n.), M. L, and ћ. write down an expression for the energies of all quantum states. (b) Find the energies of the ground state and the first three lowest lying energies. As in part (b), for each energy level, give the quantum numbers n, ny, n and...
5) A particle of mass m is in the ground state of the infinite square well 0 < x < a At t-0 the right hand wall suddenly moves to x = 2a, doubling the size of the well. Assume that this expansion happens on a time scale so fast that the initial wave function (at t0+) is the same as just before the expansion (at t-0-) (This is called the "sudden" approximation.) a) What is the probability that a...
Consider a particle in a 1-dimensional ininite square well potential {0, V(z)=Í oo, (-a < z <a) elsewhere The particle is initially localized in the right side of the well (O S a) Calculate the probability that at later times, an energy measurement will yield the energy of the first excited state of this system
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,...
An electron (mass m) is trapped ina 2-dimensional infinite square box of sides Lx - L - L. Take Eo = 92/8mL2. Consider the first four energy levels: the ground state and the first three excited states. 1) Calculate the ground-state energy in terms of Ep. (That is, the ground-state energy is what multiple of Eo? Eo Submit 2) In terms of Eo, what is the energy of the first excited state? (That is, the energy of the first excited...
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...
(a) Use the variational method to estimate the ground state energy of a particle of |mass m in a potential Vx)kx, k > 0. (b) Calculate the energy shift in the ground state and in the degenerate 1t excited state of a 2-dimensional harmonic oscillator H(P2P,2/2m m(x +y)due to the perturbation V 2Axy. (20 pts)
(a) Use the variational method to estimate the ground state energy of a particle of |mass m in a potential Vx)kx, k > 0. (b)...
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