SHO with a fixed boundary

In summary, a SHO (Simple Harmonic Oscillator) with a fixed boundary is a physical system where a particle is confined to a certain region and oscillates back and forth due to a restoring force. It exhibits periodic motion and its behavior is affected by factors such as mass, restoring force strength, and boundary size and shape. The equation of motion for a SHO with a fixed boundary is x(t) = A sin(ωt) where x is displacement, A is amplitude, ω is angular frequency, and t is time. This concept is used in various real-world applications including springs, pendulums, electronic circuits, and technologies like watches, seismographs, and musical instruments.
  • #1
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How to solve the time-independent Schodinger equation with the following potential:

U(x)=x^2 for x>x0
U(x)=infinity for x<x0 ?
 
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  • #2
To the right side of x0 it's just a harmonic oscillator potential (of which I presume you know the solutions). What's the wavefunction for x<x0? Then apply boundary conditions.
 

1. What is a SHO with a fixed boundary?

A SHO (Simple Harmonic Oscillator) with a fixed boundary is a physical system in which a particle is confined to a certain region and oscillates back and forth within that region due to a restoring force.

2. How does a SHO with a fixed boundary behave?

A SHO with a fixed boundary exhibits periodic motion, meaning it repeats the same motion over and over again. The particle moves back and forth between two points, with maximum displacement at the boundary and zero displacement at the center.

3. What factors affect the behavior of a SHO with a fixed boundary?

The behavior of a SHO with a fixed boundary is affected by its mass, the strength of the restoring force, and the size and shape of the boundary. These factors determine the frequency and amplitude of the oscillations.

4. What is the equation of motion for a SHO with a fixed boundary?

The equation of motion for a SHO with a fixed boundary is given by: x(t) = A sin(ωt), where x is the displacement of the particle, A is the amplitude of the oscillation, ω is the angular frequency, and t is time.

5. How is a SHO with a fixed boundary used in real-world applications?

SHO with a fixed boundary is a fundamental concept in physics and is used to model various systems such as springs, pendulums, and electronic circuits. It is also used in technologies such as watches, seismographs, and musical instruments.

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