Degenerate energy levels | Wikipedia audio article
Channel: wikipedia tts
Date: 24/12/2018

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Degenerate_energy_levels


00:01:03 1 Mathematics
00:03:54 2 Effect of degeneracy on the measurement of energy
00:05:57 3 Degeneracy in different dimensions
00:06:22 3.1 Degeneracy in one dimension
00:08:56 3.2 Degeneracy in two-dimensional quantum systems
00:09:47 3.3 Particle in a rectangular plane
00:15:30 3.4 Particle in a square box
00:17:26 4 Finding a unique eigenbasis in case of degeneracy
00:17:37 4.1 Choosing a complete set of commuting observables
00:17:49 4.2 Degenerate energy eigenstates and the parity operator
00:18:30 5 Degeneracy and symmetry
00:21:51 5.1 Symmetry group of the Hamiltonian
00:24:05 6 Types of degeneracy
00:27:13 6.1 Systematic or essential degeneracy
00:30:54 6.2 Accidental degeneracy
00:31:43 6.3 Examples of systems with accidental degeneracies
00:31:58 6.4 The Coulomb and Harmonic Oscillator potentials
00:32:31 6.5 Particle in a constant magnetic field
00:33:14 7 Examples
00:33:25 7.1 The hydrogen atom
00:34:10 7.2 Isotropic three-dimensional harmonic oscillator
00:34:37 8 Removing degeneracy
00:34:46 8.1 Physical examples of removal of degeneracy by a perturbation
00:38:11 8.2 Symmetry breaking in two-level systems
00:43:27 8.3 Fine-structure splitting
00:44:46 8.4 Zeeman effect
00:45:08 8.5 Stark effect
00:47:20 9 See also
00:55:34 10 References
01:00:26 11 Further reading
01:03:33 See also



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SUMMARY
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In quantum mechanics, an energy level is degenerate if it corresponds to two or more different measurable states of a quantum system. Conversely, two or more different states of a quantum mechanical system are said to be degenerate if they give the same value of energy upon measurement. The number of different states corresponding to a particular energy level is known as the degree of degeneracy of the level. It is represented mathematically by the Hamiltonian for the system having more than one linearly independent eigenstate with the same energy eigenvalue. In classical mechanics, this can be understood in terms of different possible trajectories corresponding to the same energy.
Degeneracy plays a fundamental role in quantum statistical mechanics. For an N-particle system in three dimensions, a single energy level may correspond to several different wave functions or energy states. These degenerate states at the same level are all equally probable of being filled. The number of such states gives the degeneracy of a particular energy level.