Eigenstates Definition and 188 Threads

Homework Statement We are ask to find the probability density of psi(x,t). I know that psi have an exp term but i don't understand how by squaring psi make the exp term disappear. Homework Equations Psi = sqrt(2/L)sin(n*pi*x / L)e^(-2*pi* i(E/h)t The Attempt at a Solution I...

Hello, I am a having a problem finding the solution of the follow: 3 equal masses are connected by springs in a circle, and are confined to move in the circle. Find the eigenvalues and eigenvectors of the system. I'm really at a bit of a loss here, I don't know whether you begin by...

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 am confused about operators and eigenstates. What does "an operator has two normalized eigenstates" mean ? Is there a way I can make a physical interpretation ? How are measurements made with these ?

When one says that a system is in an eigenstate of the Hamiltonian, what exactly does this mean? I mean, if the Hamiltonian is the total energy of the system, then if it is in an eigenstate of the Hamiltonian, is this saying that its energy is a multiple of its total energy? Obviously this...

Basically I have an (infinite) population of isolated atoms with a bunch of discrete energy levels available to them. I want to work out what the expected population of each of the states is at a given temperature. They're complex atoms (transition metals) and spin-orbit coupling combined...

It is common knowledge in Physics that eigenstates share the symmetries of the Hamiltonian. And it is trivial to show that this is true for the eigenspaces. Let g be an element of a symmetry group of Hamiltonian H, M_g its representation, \left| \phi \right> an eigenvector and \lambda the...

Hi people, I was asking myself... is it true that the elements of the base of solutions of the dirac equation usually used are eigenstates of elicity? Yesterday I tried the calculation following the notation of this site (it uses the dirac representation) and its set of solutions...

Quantum mechanics says measurement of observable always produces result that is one of eigenvalues of that observable. Subsequent measurement yields same value. For a particle in a box with infinite potential barriers if measure momentum doesn't that put system in eigenstate of momentum insuring...

I just started learning QM. I was wondering, if a wavefunction can only collapse onto a few eigenstates, how come the probability distribution graph is a usually continuous one? :S

Hi, i am having trouble understanding a section of a QM course concerning degenerate eigenstates. Suppose that some operator B is compatible with A (so A and B have a common eigenbasis). My notes say that this means that some r and r+pi/2 give eigenstates of both A and B in the form |a(r)> =...

Homework Statement Hi all. When riding home today from school on my bike, I was thinking about some QM. The general solution to the Schrödinger equation for t=0 is given by: \Psi(x,0)=\sum_n c_n\psi_n(x), where \psi_n(x) are the eigenfunctions of the Hamiltonian. We know that the...

It seems to be true, that if some eigenvalue of a Hamilton's operator is an isolated eigenvalue (part of discrete spectrum, not of continuous spectrum), then the corresponding eigenstate is normalizable, and on the other hand, if some eigenvalue of a Hamilton's operator is not isolated, then the...

Homework Statement I have the hamiltonian : H=C(|2><1|+|1><2|) where : C=costant |1> and |2> are eigenstates of an osservable A. what are the eigenstate and eigenvalues of the hamiltonian? what is the probability that the system is in the state |2>? The Attempt at a Solution...

I am having trouble understanding the subtleties of this topic, which we've just covered in my QM course. I guess, if I understand correctly, that the superposition of eigenstates is not necessary an eigenstate itself, unless the states are degenerate. I'm not sure if I really understand why...

Solving the time-independent Schrodinger equation gives the wavefunction for an energy eigenstate i.e. definite energy, so by the E, t uncertainty principle the uncertainty in time would be in a way "infinite". Is this what gives it the time independence? If so, how is this state physically...

Okay, so here's my knowledge of quantum mechanics: *crickets chirping in the background*. Here's my mathematical knowledge: basic integral calculus, some multivariable calculus, decent amount of linear algebra (knowledge of subspaces, projections, eigenvalues of matrices, eigenvectors, etc.), a...

Homework Statement Hi guys! Many time reader, first time poster... I've struggled big time with the following. Any advice at all would be great. I'm so muddled, it's just not funny any more... (plus I'm not really familiar with who to write the mathematic script so please be patient) I...

[SOLVED] Eigenstates and Angular Momentum Homework Statement At a given instant, a rigid rotor is in the state: \Psi(\theta,\phi)=\sqrt{\frac{3}{4\pi}}Sin(\phi) Sin(\theta) If the z component of the orbital angular momentum is measured, what are the possible values of <\hat{L_{z}}>, and...

Eigenstates: What would happen if you had a laser aimed at a mirror 45 degrees... I know this post might fit under some of the other post in this forum but i would like to ask it as a new topic because I am just getting into a lot of Quantum information ever since I noticed this part of the...

This is the way I understand it. Correct me if I'm wrong. A 'particle' in a given situation will be in a state |\psi>, which is determined by the Schrodinger Equation. After measurement, the particle will then go to a state |\omega>, where |\omega> is an eigenvector of the operator...

Problem A one dimensional particle of mass m and charge q moves on a circle of radius R. A magnetic field pierces the circle. The total magnetic flux through the circle is \Phi = B \pi R^{2}. Determine the ground state energy E_{0} (\Phi) and show that it is periodic with period \Phi_{0} =...

Homework Statement Starting with \sigma_{y}, calculate the momentum eigenstates of spin in the y direction. \sigma_{y} = \left[\stackrel{0}{i} \stackrel{-i}{0}\right] (Pauli spin matrix in the y direction) S_{y} = \frac{\hbar}{2}\sigma_{y} (spin angular momentum operator for the y direction)...

First off, what is a mass eigenstate?! Is there a (hermitian) operator associated to mass? What should I picture when discussing a non-mass-eigenstate?! The same goes for a 'weak eigenstate' as the CKM matrix is supposed to be the basis transformation between these two... :rolleyes: The I...

Hi! i want to calculate the eigenvalues and the eigenstates of the momentum operator and the Hamilton operator of a free particle. How do i do this? Thanks for answers!

Homework Statement I need to show: S^2 \left( \frac{1}{\sqrt{2}} \left[ \alpha(1) \beta(2) - \beta(1) \alpha(2) \right] \right) has an eigenvalue of zero. The attempt at a solution S_1^2 \left( \frac{1}{\sqrt{2}} \left[ \alpha(1) \beta(2) - \beta(1) \alpha(2) \right] \right)=\hbar^2...

Hi! How can I write the wave function of a particle in an infinite box (in the state n) as a superposition of the eigenstates of the momentum operator? the wave function is: PHIn(x,t) = sqrt(2/a) * Sin(n * PI/a * x) * exp(-i En/h * t) Thanks for your help!

Why is it that eigenfunctions of different excited states for 1 atom have to be orthogonal?

Homework Statement Hi, I'd doing question 1 of the attached sheet and just wondered if someone could help me out. I'm a bit unsure of my calculus and need it reviewed, alsoam not entirely sure how to break down my workings (using the supplied equations in the hint) to find C. So any input...

A couple of things first - Whats an eigenfunction? Whats an eigenvalue? I've been doing a course on quantum mechanics for nearly 2 months and whilst these words have popped up in both notes and lectures no-one has actually bothered to explain what they are or what they mean! Next thing. Can...

Hi, I have a couple of newbie questions. Are all stationery solutions to a SE eigenstates of observables? Is the converse true (that is, are all eigenstates stationery)? If the answer is no, can a measurement collapse a stationery wave-function onto a non-stationery one? And finally, is the...

I have a particle of mass m in a box of length L. The energy eigenstates of this particle have wave functions \phi_{n}(x)=\sqrt{2/L}sin(n \pi x/L) and energies E_n = n^{2}\pi^{2}\hbar^{2}/2mL^{2} where n=1, 2, 3,... At time t=0, the particle is in a state described as follows...

Consider particle of mass m in a cubic box of length L which has energy spectrum given by E=(k sqr)/2m =2 (pi sqr) (nx sqr+ ny sqr +nz sqr)/m (L sqr).what will be the density of states (eigen states per unit energy interval) k is boltzman const..nx,ny,nz are unit vectors in resp. directions...

My problem is with finding total angular momentum S of a spin 2 particles. My quantum book doesn't do any examples with spin 2 particles do i just do J(J+1)|j,m> and just plug in j and that will be my value.

Two quick ones :) Hi, two questions: 1) How can I find the expectation value of the x-component of the angular momentum, \langle L_x \rangle, when I know \langle L^2 \rangle and \langle L_z \rangle? 2) Say, I have a state |\Psi \rangle and two operators A and B represented as matrices...

Hello all, Before I start. You should note: -I'm not just looking for a solution -I've been working on this for hours -I've checked probably about 10 quantum books -I've scoured the internet -My professor can't (or won't) help me (and two other students) so I can't ask around. We three...

hi, if we have a potential of the form V(x) = a|x|, how would one go about estimating the ground state energy of the system using the Heisenberg uncertainty principle. I suppose the thing to do is to get an estimate of delta x, then get delta p via the Heisenberg uncertainty principle and...

Operators and eigenstates (updated with new question) Hi, I encountered the following HW problem which really confuses me. Could anyone please explain it to me? Thank you so much! The result of applying a Hermitian operator B to a normalized vector |1> is generally of the form: B|1> =...