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Wave funtions 
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#1
Mar506, 03:35 PM

P: 1,200

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^{kxwt}=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
Mar506, 05:05 PM

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P: 1,334

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



#3
Mar506, 05:44 PM

P: 1,200

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]



#4
Mar606, 04:32 AM

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Wave funtions
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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