Bound states Definition and 71 Threads

The current density vanishes for a bound state. I would like to know the proof and its physical significance. I appreciate the responses in advance!

Suppose a particle is subject to a spherically symmetric potential V(r) such that V(r) = -V_0, V_0 > 0, for 0\leq r \leq a and V(r) = 0 elsewhere. If we were considering a non-relativistic particle, we would have bound states for -V_0 < E < 0 (which I understand); however, since the particle is...

If I look at the energy of the hydrogen atom, the energy is proportional to the mass of the electron (or more precisely, the reduced mass). Does this mean that without a Higgs mechanism, there are no bound states of the hydrogen atom? (Or is it just an artifact of a non-relativistic theory that...

Homework Statement i have a finite square well and I have to calculate how many bound states exist in it. I have the depth and the width of the well but I cannot find an equation anywhere to help me calculate it?

Homework Statement I have to show that the delta function bound state energies can be derived from the finite square well potential. Homework Equations The wave functions in the three regions for the finite square well. (See wikipedia) The Attempt at a Solution 1. I start from the...

In all the possible potentials I have encountered so far, it seems that the bound states (i.e. E < [V(-infinity) and V(infinity)]) always results in a discrete spectrum of energies, whereas the scattering states (E > [V(-infinity) and V(infinity)]) always results in a continuous spectrum of...

Possible bound states of a one-dimensional square well... I'm Lost! Homework Statement Find the solutions of even and odd parity from the transcendental equations then find the number of bound states that are possible for a potential such that p(max) = 4? Homework Equations p=ka/2 &...

We have a potential that is (1/2)kx^2 for x>0 and is infinity for x<0 ( half harmonic oscillator. Now i want to calculate the bound states of the system for given E. My question is this: Do we apply 1. \int p(x) dx = (n - \frac{1}{4} ) h ( Since there is only one turning point that can...

Suppose I have Schroedinger equation in the form: -u''(x)+V(x)u(x)=Eu(x) The potential is such that as |x| -> Infinity, V(x) reaches a constant positive value. In this case can we have bound state/plane wave solutions for u(x) with E > 0 ?

Hello: There is a well known theorem which asserts that every attractive 1D potential has at least one bound state; in addition, this theorem does not hold for the 2D or 3D cases. I've been looking for a proof in my textbooks on qm but I've been unable to find it. Can you help me out? Thanks!

if i have a quantum well structure... and i am using infinite well approximations, how do i get the maximum number of bound states supported inside each well thnks

Hi! I'd like to ask you what do the texts mean by scattering, bound and antibound states. The context for these concepts is scattering theory. Thanks!

Homework Statement I am confused about bound states in QM. My book defines bound states as those in which the particle cannot escape to infinite. It then gives an example of a potential which is infinite when x is less than 0, -V_0 when x is between 0 and a, and 0 when x >= a. But then...

Homework Statement Hi I'm having difficulty in understanding how to calculate the radius for certain situations. for example, I have a question that asks me to calculate the radius and binding energy of muonic hydrogen. Homework Equations The Attempt at a Solution my first...

I have a question about bound states as they relate to a question on my homework... From what I can see, bound states in quantum mechanics are associated with energies that are discrete, not continuous. I don't really understand why... In my homework problem we are given a set of potential...

A recent preprint on Time in Quantum Theory ( http://www.rzuser.uni-heidelberg.de/~as3/TimeInQT.pdf ) by Dieter H Zeh has brought my attention to the question of the `speed of quantum changes'. While the classical discussions of nonlocality in Quantum Mechanics (QM) and consequences of Bell's...

Homework Statement A particle of mass m moves in three dimensions in a potential energy field V(r) = -V0 r< R 0 if r> R where r is the distance from the origin. Its eigenfunctions psi(r) are governed by \frac{\hbar^2}{2m} \nabla^2 \psi + V(r) \psi = E \psi ALL in spherical coords...

I read somewhere that quantum field theory does not allow calculations and predictions of bound states in a satisfactory way. Is that true and how much is that a problem given that qft claims to be so fundamental?

Hi, I'm working on an introductory qm project, hope somebody has the time to help me (despite the length of this post), it will be highly appreciated. My goal is to determine the bound states and their energies for the potential V_j(x) =...

To my understanding, when a particle is in a bound state, it is "stuck" because its total energy is less than the surrounding potential. I am confused on how to prove a particular potential has no bound states. For example, in one problem, I am asked to show that there is no bound state in a...

Hello,I'm physics student.I'm from Vietnam and my English is not very good. I was wondering if anyone could help me out with a question : what are scattered states and bound states ? I'm interested in "Temperature-dependent Coulomb interation in hydrogenic systems". In this...