Separation of Schrodinger Equation

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)).

The Attempt at a Solution

In the attached document

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vela
Staff Emeritus
Homework Helper

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:

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

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

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.