Degeneracy Definition and 136 Threads

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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?

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...

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...

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...

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...

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...

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...

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.

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

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...

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?

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...

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...

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...

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...

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?

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...

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...

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...

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...

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)=...

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...

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...

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...

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...

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?