# wave funtions

by UrbanXrisis
Tags: funtions, wave
 P: 1,214 I am to show that neither of the two wave functions $$\psi_1 (x,t) = M_1 e^{kx-\omega t}$$ and $$\psi_2 (x,t) = M_2 e^{i(kx-\omega t)}$$ solve the de Broglie form of Schr. Eqn: $$-\frac{\hbar ^2}{2m} \frac{\partial ^2 \psi}{\partial x^2}=i \hbar \frac{\partial \psi}{\partial t}$$ for the first wave, i got: $$-\frac{\hbar ^2}{2m} M_1 k^2 e^{kx-wt}=-i \omega \hbar M_1 e^{kx-\omega t}$$ for the second wave, i got: $$\frac{\hbar ^2}{2m} M_2 k^2 e^{i(kx-\omega t)}= \omega \hbar M_2 e^{i(kx-\omega t)}$$ i was just wondering if I did these differentiation correct.
 PF Patron HW Helper Sci Advisor P: 1,320 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
 P: 1,214 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: $$\hbar \omega = \frac{\hbar ^2 k^2}{2m}$$
HW Helper
P: 11,717

## wave funtions

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

$$p=\hbar k$$

and so $$E=\frac{p^{2}}{2m}$$

Daniel.

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