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

AI Thread Summary
The wave function of a simple harmonic wave is represented by the equation y(x,t)=Asin(ωt+kx), derived from solving Newton's second law of motion. This involves setting up a differential equation, where ω is defined as √(k/m). However, there is confusion regarding the context, as the original question pertains to classical physics rather than quantum mechanics. Some participants argue that the Schrödinger equation is not relevant for classical simple harmonic motion. The discussion highlights the ambiguity in the question and the distinction between classical and quantum harmonic oscillators.
Saxby
Messages
45
Reaction score
0
What is the wave function of a simple harmonic wave?

y(x,t)=Asin(ωt+kx)
 
Physics news on Phys.org
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 Schrodinger 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?
 
Thread 'Gauss' law seems to imply instantaneous electric field propagation'
Imagine a charged sphere at the origin connected through an open switch to a vertical grounded wire. We wish to find an expression for the horizontal component of the electric field at a distance ##\mathbf{r}## from the sphere as it discharges. By using the Lorenz gauge condition: $$\nabla \cdot \mathbf{A} + \frac{1}{c^2}\frac{\partial \phi}{\partial t}=0\tag{1}$$ we find the following retarded solutions to the Maxwell equations If we assume that...
Dear all, in an encounter of an infamous claim by Gerlich and Tscheuschner that the Greenhouse effect is inconsistent with the 2nd law of thermodynamics I came to a simple thought experiment which I wanted to share with you to check my understanding and brush up my knowledge. The thought experiment I tried to calculate through is as follows. I have a sphere (1) with radius ##r##, acting like a black body at a temperature of exactly ##T_1 = 500 K##. With Stefan-Boltzmann you can calculate...
Thread 'A scenario of non-uniform circular motion'
(All the needed diagrams are posted below) My friend came up with the following scenario. Imagine a fixed point and a perfectly rigid rod of a certain length extending radially outwards from this fixed point(it is attached to the fixed point). To the free end of the fixed rod, an object is present and it is capable of changing it's speed(by thruster say or any convenient method. And ignore any resistance). It starts with a certain speed but say it's speed continuously increases as it goes...
Back
Top