Question

(a) Write down the energy eigenvalues for a 3-dimensional oscillator with mass m and spring constant...

(a) Write down the energy eigenvalues for a 3-dimensional oscillator with mass m and spring constant kx= ky =kz and quantum number nx, ny and nz = 0, 1, 2, 3, 4 ….

(b) Write down the degeneracy of the five lowest states of a 3-dimensional harmonic oscillator in terms of nx, ny and nz.

(c) Show that the number of degeneracy of a 3-dimensional oscillator for the nth energy level is 1/2(n+1)(n+2).

Science   Advanced-Physics   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
An electron of mass m is confined to a 3-dimensional boxthat has y dimension twice that...
An electron of mass m is confined to a 3-dimensional boxthat has y dimension twice that of x or y so that it has size L x 2L x L (Lx = L, Ly = 2L and Lz = L). a) Derive an expression for the energy of each of the following bound states: (nx, ny, nz) = (1,1,1) and (2,1,1). (You do not need to use the S.E. to solve for the energy expression; use your formula sheet).Plug in...
In Classical Physics, the typical simple harmonic oscillator is a mass attached to a spring. The...
In Classical Physics, the typical simple harmonic oscillator is a mass attached to a spring. The natural frequency of vibration (radians per second) for a simple harmonic oscillator is given by ω=√k/m and it can vibrate with ANY possible energy whatsoever. Consider a mass of 135 grams attached to a spring with a spring constant of k = 1 N/m. What is the Natural Frequency (in rad/s) of vibration for this oscillator? In Quantum Mechanics, the energy levels of a...
1) A quantum harmonic oscillator with frequency ωcontains 41 electrons. What is the energy of the...
1) A quantum harmonic oscillator with frequency ωcontains 41 electrons. What is the energy of the highest-energy electron? Assume that the electrons are in the lowest states possible. 2 a) An atom has a total of 18 electrons. What is the principal quantum number of the outermost shell? 2 b) How many electrons does the outermost shell shell contain? 3) Which of the following represents the possible range of integer values for the magnetic quantum number? a) 1 to l...
Consider an electron bound in a three dimensional simple harmonic oscillator potential in the n=1 state....
Consider an electron bound in a three dimensional simple harmonic oscillator potential in the n=1 state. Recall that the e- has spin 1/2 and that the n=1 level of the oscillator has l =1. Thus, there are six states {|n=1, l=1, ml, ms} with ml= +1, 0, -1 and ms = +/- 1/2. - Using these states as a basis find the six states with definite j and mj where J = L +s - What are the energy levels...
A harmonic oscillator with mass m and force constant k is in an excited state that...
A harmonic oscillator with mass m and force constant k is in an excited state that has quantum number n. 1) Let pmax=mvmaxx, where vmax is the maximum speed calculated in the Newtonian analysis of the oscillator. Derive an expression for pmax in terms of n, ℏ, k, and m. Express your answer in terms of the variables n, k, m, and the constant ℏ 2) Derive an expression for the classical amplitude A in terms of n, ℏ, k,...
A harmonic oscillator with the usual PE of V(x)= (.5)kx^2 perturbed by a small change to...
A harmonic oscillator with the usual PE of V(x)= (.5)kx^2 perturbed by a small change to the spring constant k -->(1+E)k, with E<<1. 1. Write the new energy eigenvalues, making sure any parameters are clearly defined. 2. Expand the eigenvalue expression in a power series in E up to the second order using a Taylor series expansion. 3. What is the perturbation Hamiltonian in the problem?
Consider a one-dimensional harmonic oscillator, in an energy eigenstate initially (at t=t0), to which we apply...
Consider a one-dimensional harmonic oscillator, in an energy eigenstate initially (at t=t0), to which we apply a time dependent force F(t). Write the Heisenberg equations of motion for x and for p. Now suppose F is a constant from time t0 to time t0+τ(tau), and zero the rest of the time. Find the average position of the oscillator <x(t)> as a function of time, after the force is switched off. Find the average amount of work done by the force,...
#1: A mass of 6 kg is attached to a spring with k = 1500 N/m....
#1: A mass of 6 kg is attached to a spring with k = 1500 N/m. It is stretched a distance of 0.5 m and is released so that it oscillates in simple harmonic motion. A) What is the frequency? B) What is the energy of the oscillator? C) What is the maximum velocity for the oscillator? #2:  When at x = 0.3 m a simple harmonic oscillator (k = 2000 N/m and m = 2 kg) has a velocity of...
1 - Write the one dimensional, time-independent Schrödinger Wave Equation (SWE). Using the appropriate potential energy...
1 - Write the one dimensional, time-independent Schrödinger Wave Equation (SWE). Using the appropriate potential energy functions for the following systems, write the complete time independent SWE for: (a) a particle confined to a one-dimensional infinite square well, (b) a one-dimensional harmonic oscillator, (c) a particle incident on a step potential, and (d) a particle incident on a barrier potential of finite width. 2 - Find the normalized wavefunctions and energies for the systems in 1(a). Use these wavefunctions to...
II(20pts). Short Problems a) The lowest energy of a particle in an infinite one-dimensional potential well...
II(20pts). Short Problems a) The lowest energy of a particle in an infinite one-dimensional potential well is 4.0 eV. If the width of the well is doubled, what is its lowest energy? b) Find the distance of closest approach of a 16.0-Mev alpha particle incident on a gold foil. c) The transition from the first excited state to the ground state in potassium results in the emission of a photon with  = 310 nm. If the potassium vapor is...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT