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Okay, here's a quantum mechanics problem. I am just starting with quantum, so I have no idea about this stuff. I am requesting guidence or a push in the right direction, not nessicarily a complete answer, please. Also, I don't know if this fits into the Advanced Physics help forum. I've never posted on the homework help forum before. If this is too simple, please let me know.

A particle of mass m is in the state

[tex]\Psi (x, t) = A e^{-a[(m x^2/\hbar) + i t]}[/tex],

where A and a are positive real constants.

(a) Find A.

Shroedinger's equation?

[tex]\int_{-\infty}^{+\infty} \mid \psi \mid ^2 dx = 1[/tex]

Maybe?

I guess my plan was to take the complex conjugate of the wave function there, multiply them, and then intregrate with [tex]\int_{-\infty}^{+\infty} \mid \psi \mid ^2 dx = 1[/tex] to get the answer for A. I ran into troubles along the way, and I have some theories as to where I messed up.

Firstly, I think I took the complex conjugate incorrectly. My knowledge of complex numbers is extremely rusty :( I haven't really studied that since perhaps my sophomore year in high school...

Here's what I said it was:

[tex]\Psi^* = A e^{-a[(m x^2/\hbar) - i t]}[/tex]

So, assuming I did that correctly (which is not a very good assumption ), I moved foreward.

[tex]\mid \psi \mid ^2 = A^2 e^{-2 a m x^2/\hbar}[/tex]

Okay, and that's a gaussian, so the integration is tricky. I assume that this is not the proper way of moving foreward because when I tried to think of how to do the integration I got confused.

Does anybody have a good idea of how to move foreward with this problem?

-WraithM

## Homework Statement

A particle of mass m is in the state

[tex]\Psi (x, t) = A e^{-a[(m x^2/\hbar) + i t]}[/tex],

where A and a are positive real constants.

(a) Find A.

## Homework Equations

Shroedinger's equation?

[tex]\int_{-\infty}^{+\infty} \mid \psi \mid ^2 dx = 1[/tex]

Maybe?

## The Attempt at a Solution

I guess my plan was to take the complex conjugate of the wave function there, multiply them, and then intregrate with [tex]\int_{-\infty}^{+\infty} \mid \psi \mid ^2 dx = 1[/tex] to get the answer for A. I ran into troubles along the way, and I have some theories as to where I messed up.

Firstly, I think I took the complex conjugate incorrectly. My knowledge of complex numbers is extremely rusty :( I haven't really studied that since perhaps my sophomore year in high school...

Here's what I said it was:

[tex]\Psi^* = A e^{-a[(m x^2/\hbar) - i t]}[/tex]

So, assuming I did that correctly (which is not a very good assumption ), I moved foreward.

[tex]\mid \psi \mid ^2 = A^2 e^{-2 a m x^2/\hbar}[/tex]

Okay, and that's a gaussian, so the integration is tricky. I assume that this is not the proper way of moving foreward because when I tried to think of how to do the integration I got confused.

Does anybody have a good idea of how to move foreward with this problem?

-WraithM

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