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Homework Help: Wave Functions, Uncertainty Principle, Probability Density Function.

  1. May 17, 2009 #1
    1. The problem statement, all variables and given/known data
    Consider the wave packet defined by
    psi(x) = integral(limits of +infinity and - infinity) dke^(-alpha(k-k_0)^2) e^(ikx)

    a)What is the mean value of the momentum p barred (it's just a line over the p) of the particle in the quantum state given by this wave function
    b)What is approximately the uncertainty delta p of the momentum of the particle in this state
    c)use the integral tables to evaluate the integral psi(x) and find the probability distribution |psi(x)|^2
    d)what is the mean value of x in this state?
    e)what is the uncertainty delta x in this state?
    f)Is the heisenberg relation consistent with the values obtained for delta x and delta p

    2. Relevant equations
    delta x delta p = hbar/2 <---heisenberg uncertainty principle
    |psi(x)|^2 = 1

    3. The attempt at a solution
    Completely lost, could probably do part f, but need the preceeding parts to attempt it. I'm really very lost with quantum physics, layman's terms wouldn't be entirely wasted on me
  2. jcsd
  3. May 18, 2009 #2


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    Homework Helper

    The mean value of an operator is given by [itex]\langle \hat{A} \rangle=\langle \psi| \hat{A} | \psi \rangle=\int_{-\infty}^\infty \psi^* \hat{A} \psi dx [/itex] in the position representation. This ought to be somewhere in your text.
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