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Quantum Mechanics Complex Wave Question

  1. Oct 2, 2009 #1
    1. The problem statement, all variables and given/known data

    Consider the complex wave of amplitude;

    Psi(x,y,t) = exp[i(kxCosA + kySinA - wt)]

    Calculate the wavelength, phase velocity v, and direction of motion of this wave.


    2. Relevant equations

    Phase vel = wave length/ period or w/k


    3. The attempt at a solution

    My problem here is that this is the first wave function that I've dealt with that propogates through x, y and time. I don't know how to find the wavelength of a wave when given it's wave function. I can find the probability of it being in a certain region, or it's average position. I guess since I'm given an x, y, and time term that I'll be doing partial derivatives, especially for the phase velocity section, but my biggest problem here is not being able to even start off the problem.
     
  2. jcsd
  3. Oct 2, 2009 #2
    [tex]\vec{r}=\left(\begin{array}{c} x \\y\end{array}\right)[/tex]

    [tex]\vec{k}=k \left(\begin{array}{c} \cos A \\ \sin A \end{array}\right)[/tex]

    (note that [tex] \| \vec{k} \| = k[/tex] )

    [tex] \Psi (x,y,t)=\exp \left(k x \cos A + k y \sin A - \omega t \right) \Leftrightarrow \Psi(\vec{r},t)=\exp \left(\vec{k}.\vec{r} - \omega t \right)[/tex]

    We still have:

    [tex]\lambda = \frac{2\pi}{k}[/tex]

    and

    [tex]v = \frac{\omega}{\lambda}[/tex]
     
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