(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?