Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Free particle in one dimension

  1. May 23, 2014 #1
    I´m not sure if my way of tackling a question, probably it's a trivial problem, but it's important for me to get it right so any help will be greeted.
    The question is as follows:

    Problem: consider a particle in a one-dimensional system. The wave function ψ(x) is as follows:
    ψ(x)= 0 for (-∞<x<0),
    ψ(x)= 1/√a for (0<x<a)
    ψ(x)= 0 for (a<x<∞)

    i) if the kinetic energy is measured what is the most probable value?
    ii) which values of the momentum can never be found when measuring it?

    My reasoning:
    i) I use the operator for kinetic energy: K= -[itex]\frac{h^2}{2m}[/itex][itex]\frac{∂^2}{∂x^2}[/itex]
    which when applied: ∫ψ(x)*Kψ(x)dx gives me zero.
    If this was right I assume the most probable value of the kinetic energy is zero.
    ii) I have no clue whatsoever what the question means.

    Thanks and forgive my bad english, regards from Spain!
  2. jcsd
  3. May 23, 2014 #2


    User Avatar

    Staff: Mentor

    Hi angass, welcome to PF!

    Is that correct? Because this is not a continuous function, and therefore not a valid wave function.
  4. May 27, 2014 #3
    This looks suspiciously like a griffiths or leibowitz homework problem....

    You want to take express psi(x) in a fourier basis (as a sum of e^i(kx-wt)). Doing the fourier transform will be a simple integral from 0 to a with 1/a^1/2 as a constant.

    i) You're forgetting the edges at 0 and a. The derivative is not zero there. Once you express this function as fourier expansion, you'll see you don't get zero anymore.

    ii) apply the definition of p = i hbar d/dx to the fourier transform. The answer should drop out. I expect some of the coefficients for specific k terms in the fourier transform will be zero. (the fourier basis is an eigen value of the momentum and kinetic energy operator)
  5. May 28, 2014 #4


    Staff: Mentor

    Same here mate.

    To the OP if it is we have a homework section.

    But if it isn't - Google is your friend eg:
    http://www.colorado.edu/physics/TZD/PageProofs1/TAYL07-203-247.I.pdf [Broken]

    Last edited by a moderator: May 6, 2017
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook