# Wave equation

1. Nov 29, 2008

### Confundo

2. Nov 29, 2008

### gabbagabbahey

If $U_0(r,z)=V(r,z)e^{ikz}$, then:

$$\frac{\partial U_0}{\partial z}=\frac{\partial V}{\partial z}e^{ikz}+ikVe^{ikz}$$

due to the product rule.

so.... $$\frac{\partial^2 U_0}{\partial z^2}=\ldots$$???

3. Nov 29, 2008

### Confundo

Oops, I see now I was looking past the obvious. I'll do the calculation in the morning. Is there a reason why they leave out the $$e^{ikz}$$ from the final equation?

Thanks.

edit: $$V = V(r,z)e^{ikz}$$?

Last edited: Nov 29, 2008
4. Nov 30, 2008

### gabbagabbahey

They haven't "left it out"...To see what becomes of that term, work out the derivatives in equation (4) using the assumed form of U_0.

Huh?! ...What are you trying to ask here?

5. Nov 30, 2008

### Confundo

Worked that out now, must learn not to try and do derivatives in my head while tired.