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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 ?
U(x)=x^2 for x>x0
U(x)=infinity for x<x0 ?
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.
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.
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.
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.
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.