# Derivative of an imaginary exponential

1. Feb 13, 2006

### Shock

Does anyone know how to take the derivative of e^((x^2)/i)?

2. Feb 13, 2006

### chroot

Staff Emeritus
The derivative of eu is eudu

If u = x^2/i, find du. Substitute u and du, and you're done.

- Warren

3. Feb 13, 2006

### Shock

Bleh ya, alright, i was hoping there was a shortcut. The actual problem is much nastier, and the u substitution is giong to be hard to apply throughout.

Thanks man!

4. Feb 13, 2006

### chroot

Staff Emeritus
It isn't a very lengthy procedure.. you just have to find the derivative of u=x^2/i, which should take you only a minute, then plug it into eudu.

Do you need help with the actual problem?

- Warren

5. Feb 13, 2006

### Shock

ya actually that would be good, im still getting an imaginary left over in my <p>.

I'm trying to take a expectation value for momentum, the operator is h/i(d/dx) (hbar that is) and the actual thing im taking the derivative of is this

e^(-(ax^2)/(1+2ihat/m)) (all constants except for x) and doing what you just told me i get:

du=(-2am^2x)/(4a^2h^2t^2+m^2)+(4ia^2hmxt)/(4a^2h^2t^2+m^2)

there is also a sqrt(1+2hiat/m) under the exponential, but i want to leave that alone so i can take the intergral of x*(wavefn)^2, (the wavefn^2 i calculated in a different part of the problem, and a constant w came out of it that i need to keep everythign in terms of for this part)

So im left with an i in my expectation value for my momentum, which is wrong :(

Last edited: Feb 13, 2006
6. Feb 13, 2006

### chroot

Staff Emeritus
Are you taking the derivative of u with respect to x or t or m? I can't see how you got your du.

- Warren

7. Feb 13, 2006

### Shock

x, and my calculator did it :D

8. Feb 13, 2006

### Shock

it hasent failed me in the past, i can try doing it out by hand though to be sure

9. Feb 13, 2006

### Shock

actually, i have no clue why it got all that

10. Feb 13, 2006

### Shock

well in any case im still stuck with an imaginary momentum

11. Feb 13, 2006

### Shock

apparently <p^2>=a*(hbar)^2 LOL maybe ill try and work towards that, and see what to do, it says itll take a lot of alegbra to get it to that form though!

12. Feb 13, 2006

### Shock

still looking like an i is going to follow through, ill just go annoy the gsi (TA) about it, thanks for your help tho