Degeneracy Definition and 136 Threads

When finding a complete set of commuting observables, the goal, as I understand it, is to specify enough observables in the set such that, when given an eigenvalue of a state from each observable's matrix, these eigenvalues uniquely identify a corresponding eigenvector. It seems that every...

Homework Statement Consider a particle with mass m in the following 1D potential: V(x)=\left\{ \begin{array}{lr} mgx \ \ \ x>0 \\ \infty \ \ \ \ \ \ \ x\leq 0 \end{array} \right. What is its minimum energy calculated using the uncertainty relation? Homework Equations \Delta x \Delta p...

Homework Statement In the absence of degeneracy, prove that a sufficient condition for the equation below (1), where \left|a'\right> is an eigenket of A, et al., is (2) or (3). Homework Equations \sum_{b'} \left<c'|b'\right>\left<b'|a'\right>\left<a'|b'\right>\left<b'|c'\right> = \sum_{b',b''}...

Hi everyone! I am trying to create the density matrix for a spin-1/2 particle that is in thermal equilibrium at temperature T, and in a constant magnetic field oriented in the x-direction. This is a fairly straightforward process, but I'm getting stuck on one little part. Before starting I...

I understand that the electron degeneracy principle states that no two electrons can occupy the same space at once. However, I do not think I clearly understand the physics behind that. I talked to my physics teacher about this and he said it had to do with the electron spin; I thought it was...

Homework Statement Consider drawing one card from a deck with no jokers or other special cards. a) What is the number of microstates? (4/13/52/cant tell) b) What is the number of macrostates?(4/13/52/cant tell) c) What is the degeneracy of macrostate spade? (4/13/52/cant tell) d) What is the...

Hi everyone. I can not remember if, in 3D, the higher it is the energy level, the higher it is its degeneracy. With a cubic well and with a 3D harmonic oscillator it holds... Does anyone know if it is a general rule or not (and in the case it is, where does this rule come from)?

So I'm trying to use the excitation law of Boltzmann and the ionisation law of Saha to calculate stuff about what percentage of a quantity of hydrogen in ionised and in what energy state. I have the temperature and energy levels values, so i still need the: -statistical weight (degeneracy)...

Sometimes it happens that hamiltonian has degenerate eigenvalue. This degeneracy can be removed by modifying the Hamiltonian. If the modification is additional term proportional to an adjustable parameter, the resulting difference between the eigenvalues can be made arbitrarily small. Is...

So what I do know about degeneracy is that it's the size of an eigenspace in a certain state. How would I go about setting up the eigenspace? Let's say for a particle in the first state with n values nx = 2, ny = 1, nz = 1

Homework Statement Show that when angular momenta ##j_1## and ##j_2## are combined, the total number of states is ##(2j_1 +1)(2j_1+2)## Homework Equations The Attempt at a Solution For the two gyros in the box, there are ##2j_1 +1## possible orientations of the first gyro...

The degeneracy discriminant, that specifies the requirement for applicability of classical Maxwell-Blotzman statistics, is z<<1 where z is fugacity and z=exp^(\mu/kT). However when T\to \infty we would have z\to 1 which means we are in quantum regime while it is obvious that we are in...

Hello, I don't understand something in this exercice and i have another question:Homework Statement Use separation of variables in Cartesian coordinates to solve the infinite cubical well (or "particle in a box"): V (x, y, z) = { O,if x, y, z are all between 0 and a...

Question Particle in a box (2D) Determine the energy levels (degeneracy) of the lowest three I found that E = A (4a^2 + b^2) where A is a constant a and b are positive integers (principle quantum number) My steps I assume 4a^2 + b^2 = k where k is also a positive integer...

What is degeneracy factor? What is the degeneracy factor of photon? What is the difference between degeneracy factor and polarization of light?

Two statements that are often made about degeneracy pressure are: 1) It is a new or special kind of pressure that requires quantum mechanics, in contrast with ideal gas pressure, which in effect involves somewhat mysterious forces that emerge from the Pauli exclusion principle, and 2) it...

I have a question: is there any way to accurately "visualize" the phenomenon of electron degeneracy pressure? I understand that the main concept behind it is the Pauli Exclusion Principle. However, I was reading about the Chandrasekhar limit, and that it's derived from the fact that although a...

Hi, I have an equation of the form (-i \lambda \frac{d}{dr}\sigma_z+\Delta(r)\sigma_x) g =(\epsilon + \frac{\mu \hbar^2}{2mr^2}) g where \sigma refers to the Pauli matrices, g is a two component complex vector and the term on the right hand side of the equation is small compared to the other...

Sorry for the noob question, but is there a resource anyone can point me to for an easy to understand explanation of degeneracy pressure? I have no scientific background at all, so when I say easy I'm not kidding, but I am looking for a bit more than the pop sci bit of the Wikipedia entry...

Greetings, I was trying to prove a theorem regarding degeneracy, and I succeeded. However, I also proved the converse of the if-then part of the theorem (underlined below), which I know is wrong. I can't spot my mistake though. The theorem and my proof are written below - could someone...

Homework Statement Show that if a Hamiltonian H is invariant under all rotations, then the eigenstates of H are also eigenstates of L^{2} and they have a degeneracy of 2l+1. Homework Equations The professor told us to recall that J: \vec{L}=(L_x,L_y,L_z)...

When calculating whether Boltzmann, Bose-Einstein, or Fermi Dirac should be used there is an equation for Degeneracy Parameter A which can be initially used. Degeneracy Parameter A = (N/V) (h^2 / 2 TT m k T)^(3/2) What is represented by N and V and k? Is N the Number Density, V Volume and k...

Alright, I'm back with yet another question... So the prof was explaining that the energy in an infinite cubical well is E((h2∏2)/2ma2))(nx2+ny2+nz2) Which is all well and good, and he gave us the example of: ψ1,2,1 = E = 6((h2∏2)/2ma2)) And with little explanation mixed it up once...

Ok, I know this question will sound really stupid but I'm just not following the derivation for the formula of degeneracy's given by 1/2(n+1)(n+2) This is what I get n1+n2+n3=n so for a given n1, n2+n3=n-n1 Then this is the line I don't understand (and I'm sure its something simple I'm...

If ψ is normalize-able and a function of nx, ny, nz, is the maximum energy degeneracy 6? I.E. There can be degeneracy at the same Energy with each state taking a different value of n, yet adding up to some (nx^2+ny^2+nz^2)=Same E, due to the linearity of the operators involved. I guess the...

Homework Statement Homework Equations Below The Attempt at a Solution So this is a lot like the infinite square well, except periodic. If S is an arc length, then S = \theta R so \frac{d^2}{dS^2} = \frac{1}{R^2}\frac{d^2}{d\theta^2}, which is more convenient to use in the hamiltonian. So...

In Wikipedia this sentence is written about degeneracy; In physics, two or more different quantum states are said to be degenerate if they are all at the same energy level. Statistically this means that they are all equally probable of being filled, do you agree with the bold statement?

Hi everybody, I apologize for my trivial question, I'm reading a paper by Freedman and Kitaev and, when describing anyons and quantum Hall Effect with v=1/3, they say that "the ground state of electron liquid on the torus is 3-fold degenerate". What is the meaning? It means that there are 3...

Consider a universe where the intrinsic spin of the electron is S = 5/2, but all other parameters and Rules of Quantum Mechanics are the same. Find the degeneracy of the n=1 and n=2 levels of hydrogen. My understanding is that electrons in an atom have 4 quantum numbers n,l,ml,ms, and different...

I have just attended a talk, where the speaker (a professor in Hong Kong University) claims that neutron stars don't collapse due to "nuclear forces". He further explains that those nuclear forces are residual strong forces (i.e. exchange of pions). However, the mainstream saying (according to...

Was cosmic inflation partly driven by the quantum degeneracy pressure of the quarks and electrons? Just after the Big Bang they would all be sitting on top of each other - just what fermions don't like to do!

I am terribly confused. I have always been hearing that in the hydrogen atom, 2s and 2p orbitals have the same energy. Similarly, the 3s, 3p and 3d orbitals have the same energies. This is also suggested by the hydrogen spectrum, my professor also believes the same, and I am unable to find...

Homework Statement What is the degeneracy of the energy level E =65 E0 of the two dimensional particle in a box? Answer Homework Equations E=(h_^2/8mL^2)*(nx^2+ny^2)--> I think we use this eq. The Attempt at a Solution

Hey guys, For a particular problem I have to determine the total degeneracy across N 3-D Quantum Harmonic oscillators. Given that the degree of degeneracy for a 3-D harmonic oscillator is given by: (n+1)(n+2)/2 and the Total energy of N 3d quantum harmonic oscillators is given by...

Yesterday i had a thought about when our sun runs out of energy and collapses into a white dwarf, it is my understanding when this happens a white dwarf is held up by electron degeneracy, all the electrons are under immense pressure but cannot fall to the lowest energy state therefore stopping...

In photon statistics, g is defined as the internal degeneracy per particle, and the text gives the example that photon have two possible polarization states in three space dimensions, thus g=2. Why is the number of possible polarization equals the internal degeneracy of the particle?

Homework Statement I'm struggling to understand the concept of symmetry in quantum mechanics. My notes state "In general if the probability density has lower symmetry than the hamiltonian, the wavefunction will be degenerate". I don't really get the connection with the hamiltonian. It...

Homework Statement What is meant by the term degenerate when referring to wave function energy states? Do the wavefunctions for degenerate states necessarily look the same? Explain. Homework Equations The Attempt at a Solution Degeneracy, in terms of wave function energy states...

Firstly hello, this is the first time I have posted here (although I have used the site to find info in the past). My query is best illustrated, I think, with an example. Suppose we have some physical system with corresponding state vector \left| \psi \right> = a \left| 0 \right> + b \left|...

Can anyone explain to me what Degeneracy is properly. I know its something to do with having different eigenvalues on the same energy level or something like that, but have not been able to find a good explanation in any textbooks or anywhere online. And how does something have infinite...

the hamiltonian is H=-J \sum_{l=1}^N \sigma_l^z \sigma_{l+1}^z+ g \sigma_l^x here we assume periodic boundary condition my problem is, what is the highest possible degeneracy of the levels? initially i expected 2 but numerically i find that it is 4 i cannot understand it

Hi guys, Just got a question I'm a little stuck on and would love a push in the right direction Q) Using Hartree's theory calculate the degeneracy of the ground state of the Sodium atom. Its a previous exam question and I'm struggling to find much descriptive information about the topic...

Homework Statement In reference to the particle in an infinite, cubic well I have been asked to calculate the degeneracy of the 14th energy level and comment on its special nature. 2. The attempt at a solution Notation: E_n = E (n_x , n_y , n_z) E_14 =...

So, today while doing my homework for statistical mechanics I was reading about the quantum linear oscillator in the textbook, "Classical and Statistical Thermodynamics" by Ashley H. Carter. In it, after discussing the quantized energy it says: "Note that the energies are equally spaced and...

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)...

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...

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...

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...

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?

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...