Wave funtions

  1. I am to show that neither of the two wave functions [tex]\psi_1 (x,t) = M_1 e^{kx-\omega t}[/tex] and [tex]\psi_2 (x,t) = M_2 e^{i(kx-\omega t)}[/tex] solve the de Broglie form of Schr. Eqn:

    [tex]-\frac{\hbar ^2}{2m} \frac{\partial ^2 \psi}{\partial x^2}=i \hbar \frac{\partial \psi}{\partial t}[/tex]

    for the first wave, i got:

    [tex]-\frac{\hbar ^2}{2m} M_1 k^2 e^{kx-wt}=-i \omega \hbar M_1 e^{kx-\omega t}[/tex]

    for the second wave, i got:
    [tex]\frac{\hbar ^2}{2m} M_2 k^2 e^{i(kx-\omega t)}= \omega \hbar M_2 e^{i(kx-\omega t)}[/tex]

    i was just wondering if I did these differentiation correct.
     
  2. jcsd
  3. Physics Monkey

    Physics Monkey 1,353
    Science Advisor
    Homework Helper

    Yes, you did the differentiations correctly. I am confused by your task to show that neither function satisfies the Schrodinger equation when in fact both do as you have just shown
     
  4. well, all I have to do is to show that they are not equal. Because if i simplify both of those equations, do not get the de Broglie relation of: [tex]\hbar \omega = \frac{\hbar ^2 k^2}{2m}[/tex]
     
  5. dextercioby

    dextercioby 12,303
    Science Advisor
    Homework Helper

    What do you mean...? You do get the deBroglie relation

    [tex]p=\hbar k [/tex]

    and so [tex] E=\frac{p^{2}}{2m} [/tex]

    Daniel.
     
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