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Wave function

  1. Dec 5, 2004 #1
    hey who can help me with this physics problem?

    A particle of mass m is in the state:
    Ψ (x, t) = Aexp[-a(sqrt (mx^2) / h)-i (at / sqrt(m )) ]
    where A and a are positive real constants.
    a) Determine A.
    b) What is the frequency ƒ associated with the wave function of this particle?
    Explain your reasoning.
    c) For what potential energy function U(x), does Ψ satisfy the Schrödinger
    equation?
    d) If we use the interpretation of [Ψ(x)]^2 dx as the probability that a particle of
    mass m can be found in a region of width dx around the position x,
    calculate the expected value (average value) of the position x.


    Many thanx
     
  2. jcsd
  3. Dec 5, 2004 #2
    A. Normalize it.
    [tex]\int_{-\infty}^{+\infty} \psi^*(x) \psi(x) dx =1[/tex]
    B. Please don't make me do that. I have my own. It's probably just hard work.
    C. Differentiate it and place it in Shroedinger's equation. You'll get the potential.
    D. By definition:
    [tex]<x>=\int \psi^*(x) x \psi(x)\,dx[/tex]
     
    Last edited: Dec 5, 2004
  4. Dec 5, 2004 #3
    By "derive", you mean "differentiate" or "take the derivative", right? Those things don't mean the same as "derive".
     
  5. Dec 5, 2004 #4
    That's what I meant. You'll have to forgive me, I'm not used to saying it in English.
     
  6. Dec 5, 2004 #5

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    1.Your edited your post and now it's "differentiate".
    2.The first formula is incorrect;it has something missing:
    [tex]\int_{-\infty}^{+\infty} \psi^*(x) \psi(x) dx =1[/tex]
    The rest is correct and i agree with you.
     
  7. Dec 5, 2004 #6
    Thanks for the correction, I edited.
     
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