Separation of Schrodinger Equation

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NBaca
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Homework Statement



Show that the time-dependent Schrodinger equation is separable when V depends on time only and is uniform in space (i.e., V = V (t)).



Homework Equations





The Attempt at a Solution



In the attached document
 

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Answers and Replies

  • #2
vela
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Homework Statement



Show that the time-dependent Schrodinger equation is separable when V depends on time only and is uniform in space (i.e., V = V (t)).
Your work is fine up to here:

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

[tex]i\hbar\frac{1}{\Theta}\frac{\partial \Theta}{\partial t}-V(t)=E[/tex]

You made a simple algebra mistake in the next step of the theta equation. Your attempts to solve the differential equations are seriously misguided. These are pretty basic differential equations. You should review how to solve them.
 

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