What is Degeneracy: Definition and 147 Discussions

Electron degeneracy pressure is a particular manifestation of the more general phenomenon of quantum degeneracy pressure. The Pauli exclusion principle disallows two identical half-integer spin particles (electrons and all other fermions) from simultaneously occupying the same quantum state. The result is an emergent pressure against compression of matter into smaller volumes of space. Electron degeneracy pressure results from the same underlying mechanism that defines the electron orbital structure of elemental matter. For bulk matter with no net electric charge, the attraction between electrons and nuclei exceeds (at any scale) the mutual repulsion of electrons plus the mutual repulsion of nuclei; so in absence of electron degeneracy pressure, the matter would collapse into a single nucleus. In 1967, Freeman Dyson showed that solid matter is stabilized by quantum degeneracy pressure rather than electrostatic repulsion. Because of this, electron degeneracy creates a barrier to the gravitational collapse of dying stars and is responsible for the formation of white dwarfs.

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  1. S

    Degeneracy in a rectangular box

    A particle is confined inside a rectangular box with sides of length a,a, and 2a. What is the energy of the first excited state? Is this state degenerate? If so, determine how many different wave fuctions have this energy. The relevant equations are E=Ex+Ey+Ez =((hbar^2*pi^2)/2m)...
  2. S

    Is Degeneracy Relevant in Classical Physics and Quantum Mechanics?

    I have been told that I need to be careful to check whether degeneracy is relevant to a given problem. What does that mean? Does the concept of degeneracy exist within the framework of classical physics? Is so, which entities are degenerate? Particles? How? Is the concept of degeneracy in...
  3. cepheid

    Gravity vs. Degeneracy Pressure

    Okay, I noticed that my OP got 39 views but no responses, so let me change my strategy. Here is my question: An object made out of degenerate matter (e.g. white dwarf) will collapse if more gravitational energy is lost in getting smaller than the energy that is gained due to electron...
  4. P

    Non degeneracy of critical points

    In local coordinates what does it mean for a critical point of a function f:M\rightarrowR to be non degenerate? In addition how can you show that the definition is independent of the choice of local coordinates? I know that being a critical point is independent of the choice of local...
  5. R

    Degeneracy pressure and interactions

    hi, I wonder if the electromagnetic force is the force that expresses how pressure interacts. I mean, a pressure is a force divided by a surface. is that force the electromagnetic force, that would be the consequence of an increased kinetic energy?
  6. P

    What Is Degeneracy in Quantum Mechanics?

    First of all, I just want to check if my understanding of degeneracy is correct: The degeneracy of an excited state is the number of combinations of quantum numbers that will result in the same energy level. ? Secondly, if this is right and if we have an equation E_{xy}=\frac{\hbar^2...
  7. M

    Quark Degeneracy? String Degeneracy? (and the effect on Black Holes)

    Are there any theories that suggest that there are smaller degenerate states than the state reached in a neutron star? For example, is there a degenerate state for quarks? For strings? (should they exist) For theories that suggest such possibilities, do they discuss what would happen to the...
  8. V

    Understanding Degenerate States: Rules & Equations

    This might seem like a foolish query, but I'm having a hard time understanding the rules of degenerate states. I know that it describes how different quantum numbers lead to equal energy values, but I'm not sure how you exactly determine that. Is it just trial and error, thinking about...
  9. I

    Exploring Degeneracy in Energy Levels and Quantum Numbers in a 3D Box

    okay this isn't exactly me asking how to solve a question but just to verify the theory in my head. i need to calculate the 4 lowest energy levels for a 3d box (that has sides (2a,a,a)) and show all the quantum numbers (i imagine it means the x,y,z components of n, l, ml) and give the...
  10. H

    Degeneracy and Symmetrization Requirement

    I am encountering two-particle systems for the first time, and I am a little confused about something. Consider a infinite square well with two noninteracting particles, both fermions (though, disregard spin degrees of freedom, this is a strictly 1-d scenario). So I go to write down the...
  11. N

    Electron degeneracy pressure in QM

    In BLACK HOLES AND TIME WARPS by Kip Thorne there is a fascinating discussion about how electron degeneracy pressure fights gravity in dense stars, beginning on page 146. He says the following (abbreviated excerpts) : "..Quantum mechanics insists that when already dense matter is compressed...
  12. T

    Confused about Parity Operator & Degeneracy in Quantum Mechanics

    We're working on the parity operator in my second semester quantum mechanics class and there is one point I am confused about, either in the definition of degeneracy or in the parity operator itself. We talked about a theorem whereby the parity operator and the Hamiltonian cannot share...
  13. F

    Degeneracy and commuting observables

    Homework Statement Theorem 5 of a text I've been reading that I downloaded from online (for interested parties, the link (a pdf) is http://bohr.physics.berkeley.edu/classes/221/0708/notes/hilbert.pdf) says that "If two observables A and B commute, [A, B] = 0, then any nondegenerate eigenket...
  14. L

    Which of the four forces is responsible for degeneracy pressure?

    Actually, i have two questions: 1. Because of the Pauli exclusion principle, there can be degeneracy pressure, for instance in neutron stars, but also in electron gasses (and any fermion cluster?). What force causes this pressure? 2. According to the Pauli Exclusion principle, no two...
  15. B

    Energy Eigenstates and Degeneracy: Proving Non-Commuting Observables

    Homework Statement Two observables A_1 and A_2, which do not involve time explicitly, are known not to commute, \left[A_1,A_2\right]\ne 0 Yet they both commute with the Hamiltonian: \left[A_1,H\right]=0 \left[A_2,H\right]=0 Prove that they energy eigenstates are, in general, degenerate...
  16. S

    QM: Energy degeneracy at s=1/2 with 3 spin half particles

    I have a hamiltonian: H = J\left(\frac{1}{2\hbar^2}S_{tot}^2 - \frac{9}{8}\right) where S_{tot} = S_1 + S_2 + S_3 for 3 spin half particles in a cluster. The magnetic properties are governed entirely by their spin. I have set up the possible spin combinations from Clebsch-Gordan to be: From...
  17. I

    If a system is made of 3 atoms with no degeneracy with energy levels

    if a system is made of 3 atoms with no degeneracy with energy levels of fro example 0, e, 2e would it be safe to say that the system only has three microstate or will it be 2^3 microstates. if it is 2^3 can you please explain why?
  18. G

    Spin orbit coupling/orbital degeneracy

    disregarding the hyperfine structure and the lamb shift for the moment, spin orbit coupling says that 2S1/2 and 2P1/2 have the same energy. do 2S0 and 2P0 have the same energy? if 2P splits into 3/2 and 1/2 does the 3D orbital split into 5/2, 3/2, and 1/2 and the 4F orbital into 7/2, 5/2, 3/2...
  19. N

    Is the concept of degeneracy in quantum states always applicable?

    Hi all. When a quantum state is said to be degenerate, then it means that two states \psi_1 and \psi_2 result in the same energy and that |\psi_1|2\neq|\psi_2|2, am I correct? Now in my book we have a wavefunction given by: \psi_n =\frac{1}{\sqrt{L}}\exp(2\pi i nx/L), where n is a...
  20. F

    Chemistry: Degeneracy of states caused by multiplicity of spin

    Homework Statement For C atom (2 electrons in 2p orbital) I get L=0,1 or 2 and S=0 or 1: so spin multiplicity/terms (in braket generacy of states) are 1S(1), 3S(3), 1P(3), 3P(9), 1D(5), 3D(15)...for a total of 36 states. I am sure I am overestimating because in reality those should be...
  21. C

    Electron Degeneracy in Main Sequence Stars

    Homework Statement In main sequence stars the electrons have electron degeneracy pressure right? But if the material in the centre of the stars acts like an Ideal gas because the star is stable how is this? Are the electrons in the main sequence stars degenerate. If not then how is it that...
  22. MTd2

    Infinite Degeneracy of States in Quantum Gravity

    http://arxiv.org/PS_cache/arxiv/pdf/0811/0811.2161v1.pdf He finds that only twists and knots are conserved in ribbon networks, that is, generalized spin networks. He finds that there is an infinite number of redundant states. He suggests in the end that one might try this...
  23. Q

    Can Degenerate States be Expressed as a Linear Combination of Orthogonal States?

    Homework Statement Are all electronis states orthonormal? I mean the degenerate states ie [n,l,m>states corresponding to same energy for example can one write [2,0,0>=a[2,1,-1>+b[2,1,0>+c[2,1,+1> Homework Equations The Attempt at a Solution for example can one write...
  24. J

    Biology: how the wobble effect explains the degeneracy of the genetic code

    Hello, Here's a conceptual question: The wobble effect says that 1 tRNA can be used for more than 1 anticodon, as the nucleotide near the 5' position of the anticodon does not need to follow strict base pairing rules. The degeneracy of the genetic code refers to the fact that more than...
  25. R

    Question on Time Reversal and Degeneracy

    Under time reversal T, the momentum operator changes sign but the position operator remains the same. So if you have a Hamiltonian of the form H(X,P)=P^2 + V(X) , then it's invariant under time reversal since momentum is squared. This means H and T commute, so that if a state has eigenvalue E of...
  26. O

    Hamiltonian & Degeneracy: Conditions

    Hi all, could someone give me a quick answer on the exact conditions for the hamiltonian to be non degenerate, i.e. to have different eigenvalues? thanks in advance.
  27. L

    What Causes Degeneracy Pressure?

    I was wondering something, a collection of fermions can resist compressing forces due to what is termed degeneracy pressure. I was wondering, which of the four fundamental interactions is this due to? Thanks. Molu
  28. S

    Degeneracy of rotationally invariant potentials

    I can appreciate the degeneracy of an infinite cubical well, in which there are three different directions, and hence three different separation constants from Schrodinger's equation which determine three separate n's (for lack of a better word.. principal quantum numbers, i suppose. it really...
  29. E

    Can someone explain the idea of degeneracy of orbitals?

    This is a confusing topic. What does it mean to be degenerate? How does this apply to atomic orbitals versus molecular orbitals? Can you point me to a good reference book on the subject?
  30. J

    2-dimensional valley degeneracy

    I was about to do a simulation on www.nanohub.org on a MOSFET when the simulation program asked me for the valley degeneracy of the 2DEG. I've tried to look this up but i can't find it anywhere. Does somebody know a website where I can find the valley degeneracy for a 2DEG for Si, GaAs, InAs...
  31. CJames

    Neutron degeneracy pressure and electron degeneracy pressure

    The words neutron degeneracy pressure and electron degeneracy pressure are thrown around a lot when talk of white dwarfs, neutron stars, and black holes comes up. Despite this, I can't find a quantitative description of these critical pressures ANYWHERE. It is almost always described in terms of...
  32. N

    Determine the energy levels, their degeneracy and wave functions of a particle

    Homework Statement Determine the energy levels, their degeneracy and wave functions (in ket notation) of a particle with spin quantum number s =1 if the Hamiltonian is AS_x^2 + AS_y^2 + B S_z^2 where A and B are constants. The Attempt at a Solution' I've spent ages thinking about this...
  33. M

    Deducing Degeneracy in Spin from Commutation Relations

    In reviewing the derivation of the quantization of angular momentum-like operators from their commutation relations, I noticed that there is nothing a priori from which you can deduce the degeneracy of the eigenstates. While this is not a problem for angular momentum, in which other constraints...
  34. A

    Degeneracy of multiple electron states

    Homework Statement A seemingly trivial part of a Homework I've gotten is to find the degeneracy of the {}^1\! S_0, {}^1\! D_2, {}^3\! P_2, {}^3\! P_1, {}^3\! P_0 in an O^{++} ion. Homework Equations The Attempt at a Solution an O^{++} ion has 4 valance electrons and when \ell=1 for...
  35. M

    Degeneracy of the 3d harmonic oscillator

    Hi! I'm trying to calculate the degeneracy of each state for 3D harmonic oscillator. The eigenvalues are En = (N + 3/2) hw Unfortunately I didn't find this topic in my textbook. Can somebody help me?
  36. P

    What is Degeneracy of Dark Matter?

    Hi everyone - I'm having some trouble with the real concept behind "degeneracy" of dark matter. I've heard of degeneracy before in maths (eg. a 'point' is a degenerate 'circle'), and in physics (eg. energy level degeneracy in atom shells), but I don't quite see how either of these work when...
  37. J

    Degeneracy in 3-D Rectangular Boxes: Explained

    This isn't a homework question, rather a question about something stated in my book and an online source. When is there degeracy in a 3-D rectangular box when none of the sides are of equal length? I understand that when there are two or more state functions that have same energy level...
  38. A

    Hydrogen Degeneracy: Qualitative Explanation

    The hydrogen energy levels (when only considering the coulomb field of an infinitely massive proton - or when using the reduced mass for the electron) only depend on the principle quantum number n. Can someone give me a qualitative argument why the orbital angular momentum quantum number l...
  39. J

    What is the degeneracy of the ground state

    H=\frac{p^2}{2m'}+V_0(r)+V(r) where V(r)=2[3\frac{(S \cdot r)^2}{r^2}-S^2] and V_0(r) is a rotationally invariant potential, p=p1-p2, the relative momentum and m' the reduced mass. S=S1+S2 spin operator. Assume first that V(r) is zero; what is the degeneracy of the ground state...
  40. D

    Degeneracy conduction electrons

    I'm supposed to show that the degeneracy of the energy levels of conduction electrons at fixed k_z[/tex] in zero magnetic field is given by \frac{2L_x L_y}{\pi \hbar ^2} m \mu _B B Where the energy levels of the electrons are of the form (approximation): E_{n,n_z} = E_n(k_z)=...
  41. Clausius2

    Rotation Energy Levels and Degeneracy.

    Solving the Schrödinger equation in spherical coordinates for a diatomic gas, one finds that the rotational energy leves are given by: \epsilon_l=K\cdot l(l+1) where l=0,1,2... is the rotational quantum number and K is a constant. It is said that each energy level shows a degeneracy of...
  42. D

    What are the implications of Ansari's discovery of degeneracy in LQG?

    Recently, I read a beautiful paper in which it is proven that ANY surface in LQG contains degeneracy, no matter it being a boundary horizon or whatever else. (http://uk.arxiv.org/abs/gr-qc/0603121) This degeneracy is such that the surface degeneracy is A/4. This is a critial discovery in LQG and...
  43. Q

    Valley Degeneracy of Semiconductor Band Systems

    Hiya, trying to learn something about the band system of semiconductors, I found that the conduction band is degenerated at the minimum by valley degeneracy. Do you know where this comes from? In how far is it dependent of the form of the band gap (i.e. direct, indirect)? I would be...
  44. O

    How Do Term Symbols Reflect Electron Spin States and Degeneracy?

    Hi! I've finally made some effort to understand spectroscopic term symbols (^{2S+1}L_J) and after having thought a few times that I'd understood but then running into trouble again, now I'm fairly convinced that I got it right. But some things bother me though. Apparently I was locked too...
  45. S

    Solving Degeneracy Equation: General Formula & More

    Hello all. I'm presently on my first set of homework for my 2nd QM class, and am stuck on the degeneracy issue. I thought that I had a more comprehensive explanation of it in my notes from the first semester, but was not able to find them. I know that I'm suppposed to take the sum of the...
  46. K

    Can dark energy prevent neutron stars from collapsing into black holes?

    How can gravity overcome the degeneracy pressure of neutrons in a neutron star? Isn't such a thing the same as violating the uncertainty principle?
  47. M

    Two fold degeneracy perturbation question

    consider a two fold degeneracy such that H Psi_a = E Psi_a and H Psi_b = E Psi_b and <Psi_a | Psi_b> = 0 All of the above are the unperturbed states, Hamiltonian and eigenvalue. Notice the two states share the eigen value E. Form the linear combination of the two states Psi = a *...
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