# I Alternate form of wave equation

1. Nov 11, 2017

### Daniel Sellers

Apologies if this question is better posed in the mathematics section, it is for a quantum mechanics class so I decided to post it here:

We are asked to verify that the following equation is a solution to the Schrodinger wave equation for a free particle:

Psi(x,t) = Ae^i(kx-wt) - Ae^-i(kx+wt)

I did that part just fine, but then we are asked to show that this wave equation can be rewritten as

Psi(x,t) = 2AiSinkxe^(-iwt)

and answer the question: What kind of wave of this?

So far the only thing I can come up with is

Psi(x,t) = 2AiSin(kx)cost(wt)

Which doesn't seem compatible at all.

Can anyone show me how this is the same equation? and if you know 'what kind of wave' this is that would be very helpful too.

2. Nov 11, 2017

### Staff: Mentor

Try rewriting $e^{i(kx - wt)}$ and $e^{-i(kx + wt)}$ as products of exponentials. Pay careful attention to the signs of the $wt$ terms in the exponentials.

3. Nov 12, 2017

### Daniel Sellers

In fact, that works! Thanks very much!

Now I just need to figure out what the problem means when it asks what type of wave this is and I'll be set.