(a) Using the separation of variables technique, and letting the separation constant be denoted

**E** (which turns out to be the total energy of the particle), show that the resulting differential equation that is

*independent* of time—the so-called

**time-independent Schroedinger equation (TISE)**—has the (1-D) form

where we have set

.

This I have done this already... And I've narrowed down to these two differential equations:

The one above

(b) Also, show that the total wavefunction in this case has the form

Here's what I did:

This looks only similar to the actual solution for T(t)... What am I doing wrong?