Understanding SHM: Calculating the Wave Function of a Simple Harmonic Wave

[Saxby]

What is the wave function of a simple harmonic wave?

y(x,t)=Asin(ωt+kx)

 

[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..

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

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

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

I'm not sure if this answers your question?

 

[Jorriss]

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..

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

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

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

I'm not sure if this answers your question?

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

 

[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.

 

[Jorriss]

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.

Fair enough, it is a bit ambiguous eh?