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

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Discussion Overview

The discussion centers around the wave function of a simple harmonic wave, specifically the equation y(x,t)=Asin(ωt+kx). Participants explore the derivation of this equation, its relation to classical mechanics, and the distinction between classical and quantum harmonic oscillators.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents the wave function y(x,t)=Asin(ωt+kx) as the equation of motion for a simple harmonic oscillator, derived from Newton's force law.
  • Another participant reiterates the derivation of the wave function from Newton's laws, expressing uncertainty about whether this fully addresses the original question.
  • A different participant argues that the original question pertains to the wave function, suggesting that the Schrödinger equation should be used instead of Newton's laws.
  • Some participants note that the discussion is framed within classical physics, indicating that the context of simple harmonic motion does not necessitate quantum mechanical considerations.
  • There is acknowledgment of ambiguity in the question posed, suggesting differing interpretations of what is meant by "wave function."

Areas of Agreement / Disagreement

Participants express disagreement regarding the appropriate framework for discussing the wave function, with some advocating for classical mechanics and others suggesting a quantum approach. The discussion remains unresolved regarding the correct interpretation and application of the wave function in this context.

Contextual Notes

The discussion highlights the ambiguity in the terminology used, particularly regarding the distinction between classical and quantum harmonic oscillators. There is also a lack of consensus on the relevance of the Schrödinger equation in this context.

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What is the wave function of a simple harmonic wave?

y(x,t)=Asin(ωt+kx)
 
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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?
 
Last edited:
sleepycoffee said:
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.
 
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.
 
sleepycoffee said:
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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