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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..

[itex] F=ma=-kx \\
ma+kx=0 \\
a+\frac{k}{m}x=0 [/itex]
Or you can write

[itex] \ddot{x}+\frac{k}{m}x=0 [/itex]

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

I'm not sure if this answers your question?

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..

[itex] F=ma=-kx \\
ma+kx=0 \\
a+\frac{k}{m}x=0 [/itex]
Or you can write

[itex] \ddot{x}+\frac{k}{m}x=0 [/itex]

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

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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