Wave function in SHM

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..

[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

Quote by 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..

[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

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

Quote by 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.

Fair enough, it is a bit ambiguous eh?

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Saxby Recognitions: Gold Member	Wave function in SHM Tweet 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.. [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?

sleepycoffee	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.