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-   -   Wave function in SHM (http://www.physicsforums.com/showthread.php?t=672678)

 Saxby Feb18-13 12:24 PM

Wave function in SHM

What is the wave function of a simple harmonic wave?

y(x,t)=Asin(ωt+kx)

 sleepycoffee Feb18-13 01:25 PM

Re: Wave function in SHM

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 $\omega = \sqrt{\frac{k}{m}}$.

 Jorriss Feb18-13 05:28 PM

Re: Wave function in SHM

Quote:
 Quote by sleepycoffee (Post 4275334) 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 $\omega = \sqrt{\frac{k}{m}}$. I'm not sure if this answers your question?
He was asking for the wave function. You need to solve it with the Schrodinger equation, not Newtons laws.

 sleepycoffee Feb19-13 01:45 AM

Re: Wave function in SHM

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 Feb19-13 08:07 AM

Re: Wave function in SHM

Quote:
 Quote by sleepycoffee (Post 4276274) 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?

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