Table of Contents

## What is the energy of harmonic oscillator?

In a simple harmonic oscillator, the energy oscillates between kinetic energy of the mass K = 12mv2 and potential energy U = 12kx2 stored in the spring. In the SHM of the mass and spring system, there are no dissipative forces, so the total energy is the sum of the potential energy and kinetic energy.

### How do you find the degeneracy of a harmonic oscillator?

1 Answer

1. For the 3-D isotropic oscillator the energy levels are given by.
2. EN = Ek + El + Em = (3/2 + nk + nl + nm)ℏω
3. where ω is the angular frequency.
4. N = nk + nl + nm = 0, 1, 2 …
5. For a given value of N, various possible combinations of nk , nl and nm are given in Table 3.5, and the degeneracy indicated.

What is degeneracy in harmonic oscillator?

Quantum degeneracy just means that more than one quantum states have exactly the same energy. A linear (1-D) simple harmonic oscillator (e.g. a mass-on-spring in 1-D) does not have any degenerate states. However in higher dimension harmonic oscillators do show degeneracy.

What is degenerate perturbation?

The perturbation expansion has a problem for states very close in energy. The energy difference in the denominators goes to zero and the corrections are no longer small. The series does not converge.

## What is the total energy of a simple harmonic oscillator?

At the mean position, the velocity of the particle in S.H.M. is maximum and displacement is minimum, that is, x=0. Therefore, P.E. =1/2 K x2 = 0 and K.E. = 1/2 k ( a2 – x2) = 1/2 k ( a2 – o2) = 1/2 ka2. Thus, the total energy in simple harmonic motion is purely kinetic.

### How do you find the ground state energy of a harmonic oscillator?

NOTE The ground-state energy of the quantum harmonic oscillator is E, = 2hw. An atomic mass on a spring can not be brought to rest. This is a consequence of the uncertainty principle. FIGURE 41.21 shows the first three energy levels and wave functions of a quantum harmonic oscillator.

Which of the following are degenerate energy levels?

Degenerate orbitals are the orbitals of the same subshell of the same main shell. Hence, these are (3dxy,3dz,3dyz) and (4dxy,4dyz,4dz).

What is meant by degenerate and non degenerate perturbation?

Recall that degeneracy in quantum mechanics refers to the situation when more than one eigenstate corresponds to the same energy. Conversely, non-degeneracy occurs when each eigenstate corresponds to a unique energy.

## What is degenerate eigenvalue?

An eigenvalue is degenerate if there is more than one linearly independent eigenstate belong- ing to the same eigenvalue. Degeneracy occurs both in classical and quantum mechanical problems and is almost always related to some spatial symmetry of the system.