1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Particle in One-Dimensional Box Problem [Quantum Mechanics]

  1. Mar 9, 2016 #1
    The problem statement, all variables and given/known data
    a) Determine the ratio (Em/En) between two energy states of a particle in a one dimensional box of length l.
    b) Show that this is consistent with the non-relativistic low-energy limit.

    The attempt at a solution

    I have figured out a) using the de broglie wave-particle duality and the energy momentum relationship to get:
    Em/En = m2/n2 but I am unsure what this non-relativistic low-energy limit is.
    I though about using classical kinetic energy to (ie. non-relativistic) of the particle and using similar equations (de broglie wavelength, standing wave) but I realized using the assumption of a De Broglie wavelength implies its accordance with relativity and I find myself somewhat lost.
     
  2. jcsd
  3. Mar 10, 2016 #2
    one should take a one dimensional box say of length L and write out the schrodinger equation -then calculate the wave function -apply the boundary condition at L=0 and L=L, the wave function must vanish at the boundary as the particle is confined.
    that should yield the energy eigen values - take the ratio of two states say mth and nth state its a non relativistic situation.
    check the energy ratio .
     
  4. Mar 10, 2016 #3

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    What's this energy momentum relationship you refer to?

    I don't think the assumption of a de Broglie wavelength implies SR. Why do you think it does?
     
  5. Mar 11, 2016 #4
    You should solve it as drvrm described. Using the assumption of a De Broglie wavelength implies that the particle is free (no potential), your particle is free only inside the box.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Particle in One-Dimensional Box Problem [Quantum Mechanics]
Loading...