# Wave function in SHM

1. Feb 18, 2013

### Saxby

What is the wave function of a simple harmonic wave?

y(x,t)=Asin(ωt+kx)

2. Feb 18, 2013

### sleepycoffee

y(x,t)=Asin(ωt+kx) is the equation of motion for a simple harmonic oscillator.

You get this by solving Newton's force law..

$F=ma=-kx \\ ma+kx=0 \\ a+\frac{k}{m}x=0$
Or you can write

$\ddot{x}+\frac{k}{m}x=0$

This is a differential equation, solved by Asin(ωt+kx), where $\omega = \sqrt{\frac{k}{m}}$.

Last edited: Feb 18, 2013
3. Feb 18, 2013

### Jorriss

He was asking for the wave function. You need to solve it with the Schrodinger equation, not Newtons laws.

4. Feb 19, 2013

### sleepycoffee

This is posted in classical physics, however.. and in any case if it is undergoing simple harmonic motion then it isn't a quantum harmonic oscillator, so I don't see any reason to be messing around with Schrodingers.

5. Feb 19, 2013

### Jorriss

Fair enough, it is a bit ambiguous eh?