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3. Consider a particle of mass m moving in a potential given by: W (2, y,...
3. A particle is in a 1D box (infinite potential well) of dimension, a, situated symmetrically ab...
3. A particle is in a 1D box (infinite potential well) of dimension, a, situated symmetrically about the origin of the x-axis. A measurement of energy is made and the particle is found to have the ground state energy: 2ma The walls of the box are expanded instantaneously, doubling the well width symmetrically about the origin, leaving the particle in the same state. a) Sketch the initial potential well making it symmetric about x - 0 (note this is different...
3.9. A particle of mass m is confined in the potential well 0 0<x < L...
3.9. A particle of mass m is confined in the potential well 0 0<x < L oo elsewhere (a) At time t 0, the wave function for the particle is the one given in Problem 3.3. Calculate the probability that a measurement of the energy yields the value En, one of the allowed energies for a particle in the box. What are the numerical values for the probabilities of obtaining the ground-state energy E1 and the first-excited-state energy E2? Note:...
A particle with mass m is in a one-dimensional simple harmonic oscillator potential. At time t = 0 it is described by the state where lo and l) are normalised energy eigenfunctions corresponding to e...
A particle with mass m is in a one-dimensional simple harmonic oscillator potential. At time t = 0 it is described by the state where lo and l) are normalised energy eigenfunctions corresponding to energies E and Ey and b and c are real constants. (a) Find b and c so that (x) is as large as possible. b) Write down the wavefunction of this particle at a time t later c)Caleulate (x) for the particle at time t (d)...
please solve with explanations 3. (20 pts) A particle of mass m and charge q is in a one dimensional harmonic oscillato...
please solve with explanations
3. (20 pts) A particle of mass m and charge q is in a one dimensional harmonic oscillator potential ()1ma'. A time dependent uniform electric field E, ()E, os eris 2 applied in the x direction. The particle is in the harmonic oscillator ground state at time a) What is the time dependent perturbation Hamiltonian H'(t) - the potential enegy of the charge in this electric field? b) Find the amplitude ci(t) of finding the particle...
Consider a particle subjected to a harmonic oscillator potential of the form x)m. The allowed values...
Consider a particle subjected to a harmonic oscillator potential of the form x)m. The allowed values of energy for the simple harmonic oscillator is (a) What is the energy corresponding to the ground state (3 points)? (b) What is the energy separation between the ground state and the first excited state (3 points)? (c) The selection rule allows only those transitions for which the quantum number changes by 1. What is the energy of photon necessary to make the transition...
A For a particle with mass m moving under a one dimensional potential V(x), one solution...
A For a particle with mass m moving under a one dimensional potential V(x), one solution to the Schrödinger equation for the region 0<x< oo is x) =2 (a>0), where A is the normalization constant. The energy of the particle in the given state is 0, Show that this function is a solution, and find the corresponding potential V(x)?
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...
3. A particle with mass m and charge q moves in a uniform magnetic filed of...
3. A particle with mass m and charge q moves in a uniform magnetic filed of magnitude B that is oriented along the z axis. (a) Neglecting the effects of spin and using the so-called Landau gauge with the vector po- tential given by A = (-By,0,0), show that the Hamiltonian may be written as À = 2m 2 ++øp +29BD2y +(, 2] (1) с (b) Because Pa and Êz commute with Ĥ, the time-independent Schrödinger equation for (x, y,...
[12 6. Consid er a particle of mass m moving in an infinitely deep square well...
[12 6. Consid er a particle of mass m moving in an infinitely deep square well potential of width a, whose wave function at time t 0 is where on Ce) is the normaized wave function of the n-th eigenstate of the Hamitonian of that particle The corresponding eigen-energy of the n-th state is 2ma?n 1,2,3,... (e) Find the average energy of the system (ie. the expectation value () (b) Write down the wave function p(z,t) at a later time...
1. Consider a spin-0 particle of mass m and charge q moving in a symmetric three-dimensional harm...
1. Consider a spin-0 particle of mass m and charge q moving in a symmetric three-dimensional harmonic oscillator potential with natural frequency W.Att-0 an external magnetic field is turned on which is uniform in space but oscillates with temporal frequency W as follows. E(t)-Bo sin(at) At time t>0, the perturbation is turned off. Assuming that the system starts off at t-0 in the ground state, apply time-dependent perturbation theory to estimate the probability that the system ends up in an...
3. A particle is in a 1D box (infinite potential well) of dimension, a, situated symmetrically about the origin of the x-axis. A measurement of energy is made and the particle is found to have the ground state energy: 2ma The walls of the box are expanded instantaneously, doubling the well width symmetrically about the origin, leaving the particle in the same state. a) Sketch the initial potential well making it symmetric about x - 0 (note this is different...
3.9. A particle of mass m is confined in the potential well 0 0<x < L oo elsewhere (a) At time t 0, the wave function for the particle is the one given in Problem 3.3. Calculate the probability that a measurement of the energy yields the value En, one of the allowed energies for a particle in the box. What are the numerical values for the probabilities of obtaining the ground-state energy E1 and the first-excited-state energy E2? Note:...
A particle with mass m is in a one-dimensional simple harmonic oscillator potential. At time t = 0 it is described by the state where lo and l) are normalised energy eigenfunctions corresponding to energies E and Ey and b and c are real constants. (a) Find b and c so that (x) is as large as possible. b) Write down the wavefunction of this particle at a time t later c)Caleulate (x) for the particle at time t (d)...
please solve with explanations
3. (20 pts) A particle of mass m and charge q is in a one dimensional harmonic oscillator potential ()1ma'. A time dependent uniform electric field E, ()E, os eris 2 applied in the x direction. The particle is in the harmonic oscillator ground state at time a) What is the time dependent perturbation Hamiltonian H'(t) - the potential enegy of the charge in this electric field? b) Find the amplitude ci(t) of finding the particle...
Consider a particle subjected to a harmonic oscillator potential of the form x)m. The allowed values of energy for the simple harmonic oscillator is (a) What is the energy corresponding to the ground state (3 points)? (b) What is the energy separation between the ground state and the first excited state (3 points)? (c) The selection rule allows only those transitions for which the quantum number changes by 1. What is the energy of photon necessary to make the transition...
A For a particle with mass m moving under a one dimensional potential V(x), one solution to the Schrödinger equation for the region 0<x< oo is x) =2 (a>0), where A is the normalization constant. The energy of the particle in the given state is 0, Show that this function is a solution, and find the corresponding potential V(x)?
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...
3. A particle with mass m and charge q moves in a uniform magnetic filed of magnitude B that is oriented along the z axis. (a) Neglecting the effects of spin and using the so-called Landau gauge with the vector po- tential given by A = (-By,0,0), show that the Hamiltonian may be written as À = 2m 2 ++øp +29BD2y +(, 2] (1) с (b) Because Pa and Êz commute with Ĥ, the time-independent Schrödinger equation for (x, y,...
[12 6. Consid er a particle of mass m moving in an infinitely deep square well potential of width a, whose wave function at time t 0 is where on Ce) is the normaized wave function of the n-th eigenstate of the Hamitonian of that particle The corresponding eigen-energy of the n-th state is 2ma?n 1,2,3,... (e) Find the average energy of the system (ie. the expectation value () (b) Write down the wave function p(z,t) at a later time...
1. Consider a spin-0 particle of mass m and charge q moving in a symmetric three-dimensional harmonic oscillator potential with natural frequency W.Att-0 an external magnetic field is turned on which is uniform in space but oscillates with temporal frequency W as follows. E(t)-Bo sin(at) At time t>0, the perturbation is turned off. Assuming that the system starts off at t-0 in the ground state, apply time-dependent perturbation theory to estimate the probability that the system ends up in an...
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