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Saxby
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What is the wave function of a simple harmonic wave?
y(x,t)=Asin(ωt+kx)
y(x,t)=Asin(ωt+kx)
He was asking for the wave function. You need to solve it with the Schrodinger equation, not Newtons laws.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..
[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?
Fair enough, it is a bit ambiguous eh?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.
SHM stands for Simple Harmonic Motion. It is a type of periodic motion in which an object oscillates back and forth around an equilibrium point, following a sinusoidal pattern.
A wave function, also known as a displacement function, is a mathematical representation of a wave. It describes the displacement of a wave at a certain point in space and time.
The wave function of a simple harmonic wave can be calculated by using the equation y = A*sin(ωt + φ), where A is the amplitude, ω is the angular frequency, t is the time, and φ is the phase angle. The wave function can also be represented in terms of the wave's wavelength and frequency.
In SHM, the frequency and wavelength of a wave are inversely proportional. This means that as the frequency increases, the wavelength decreases, and vice versa. This relationship is described by the equation f = c/λ, where f is frequency, c is the speed of the wave, and λ is the wavelength.
SHM is closely related to other types of motion, such as circular motion and simple pendulum motion. In fact, SHM can be thought of as a combination of these two types of motion. For example, an object on a spring moving up and down can be seen as a combination of circular motion around the equilibrium point and pendulum motion back and forth.