# Wave function

1. Dec 5, 2004

### mlee

hey who can help me with this physics problem?

A particle of mass m is in the state:
Ψ (x, t) = Aexp[-a(sqrt (mx^2) / h)-i (at / sqrt(m )) ]
where A and a are positive real constants.
a) Determine A.
b) What is the frequency ƒ associated with the wave function of this particle?
c) For what potential energy function U(x), does Ψ satisfy the Schrödinger
equation?
d) If we use the interpretation of [Ψ(x)]^2 dx as the probability that a particle of
mass m can be found in a region of width dx around the position x,
calculate the expected value (average value) of the position x.

Many thanx

2. Dec 5, 2004

### Palindrom

A. Normalize it.
$$\int_{-\infty}^{+\infty} \psi^*(x) \psi(x) dx =1$$
B. Please don't make me do that. I have my own. It's probably just hard work.
C. Differentiate it and place it in Shroedinger's equation. You'll get the potential.
D. By definition:
$$<x>=\int \psi^*(x) x \psi(x)\,dx$$

Last edited: Dec 5, 2004
3. Dec 5, 2004

### Nylex

By "derive", you mean "differentiate" or "take the derivative", right? Those things don't mean the same as "derive".

4. Dec 5, 2004

### Palindrom

That's what I meant. You'll have to forgive me, I'm not used to saying it in English.

5. Dec 5, 2004

### dextercioby

$$\int_{-\infty}^{+\infty} \psi^*(x) \psi(x) dx =1$$