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Homework Help: QM: 1D infinite square well

  1. Mar 23, 2009 #1
    1. The problem statement, all variables and given/known data

    A particle of mass m is in a one-dimensional infinite square well that extends from x = –a to x = a.

    a) Find the energy eigenfunctions ψn (x) and corresponding eigenvalues En of this particle. (Hint: you may use the results of the book for an infinite square well between x=0 and x=a, appropriately modified!)

    b) The parity operator Π is defined as: Π ψ(x) = ψ (–x) for any function ψ(x). Does Π commute with the Hamiltonian H of this particle?

    c) Are the energy eigenfunctions ψn (x) also eigenfunctions of Π and, if yes, with what eigenvalue each?

    The wavefunction of the particle at some initial time is ψ = C sin |πx/a| , with C a real positive constant. ( ψ = 0 for |x| > a )

    d) Normailize the wavefunction by calculating the appropriate value of C.

    e) Calculate the expectation value of the energy of this particle.

    f) Is the above wavefunction an eigenfunction of Π and, if yes, with what eigenvalue?

    g) What is the probability that a measurement of the energy of this particle will yield the value E2 ? (Hint: the result of (c) and (f) may help you.)

    Can anyone help me with this? Thanks.
  2. jcsd
  3. Mar 23, 2009 #2

    I would like to help you, but please give it a try first, then we can look at it together.
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