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Separation of Schrodinger Equation

  • Thread starter 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)).



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The Attempt at a Solution



In the attached document
 

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  • #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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