Homework Help: Separation of Schrodinger Equation

1. Mar 31, 2010

NBaca

1. The problem statement, all variables and given/known data

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)).

2. Relevant equations

3. The attempt at a solution

In the attached document

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2. Mar 31, 2010

vela

Staff Emeritus
Your work is fine up to here:

$$-\frac{\hbar^2}{2m}\frac{\partial^2\psi}{\partial x^2}=E\psi$$

$$i\hbar\frac{1}{\Theta}\frac{\partial \Theta}{\partial t}-V(t)=E$$

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.