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

In summary, the wave function of a simple harmonic wave is given by the equation y(x,t)=Asin(ωt+kx), derived from solving Newton's force law. It can also be written as \ddot{x}+\frac{k}{m}x=0 and solved using the Schrodinger equation with \omega = \sqrt{\frac{k}{m}}. However, if the system is undergoing simple harmonic motion, there is no need to use the Schrodinger equation as it is a classical physics concept.
  • #1
Saxby
45
0
What is the wave function of a simple harmonic wave?

y(x,t)=Asin(ωt+kx)
 
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  • #2
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?
 
Last edited:
  • #3
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?
He was asking for the wave function. You need to solve it with the Schrodinger equation, not Newtons laws.
 
  • #4
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.
 
  • #5
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?
 

What is SHM?

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.

What is a wave function?

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.

How do you calculate the wave function of a simple harmonic wave?

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.

What is the relationship between frequency and wavelength in SHM?

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.

How is SHM related to other types of motion?

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.

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