Verifying Solutions of de Broglie Form of Schr. Eqn

[UrbanXrisis]

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.

 

[Physics Monkey]

Yes, you did the differentiations correctly. I am confused by your task to show that neither function satisfies the Schrödinger equation when in fact both do as you have just shown

 

[UrbanXrisis]

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: $$\hbar \omega = \frac{\hbar ^2 k^2}{2m}$$

 

[dextercioby]

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

$$p=\hbar k$$

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

Daniel.