Particle in a box and the Harmonic Oscillator
This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!
Please read the attached file for complete description of the problem.
Consider the particle of mass subject to a one-dimensional potential of the following form:
V(x) = 1/2 kx^2 for x>0
V(x) = + infinity for x < 0
This is a combination of the particle in a box and the harmonic oscillator that might be a better model for real diatomic than the standard harmonic oscillator. On the right side of x = 0, the Hamiltonian is exactly the same as a harmonic oscillator Hamiltonian. The hard wall at x = 0, however, introduces a boundary condition. Use what you have learned about both the ordinary harmonic oscillator and particle in a box boundary conditions to answer the following questions.
a) what does this boundary condition require the wave function to do at x = 0?
Following is the text part of the solution. Please see the attached file for complete solution. Equations, diagrams, graphs and special characters will not appear correctly here. Thank you for using Brainmass.
a. Boundary condition is that at x = 0, Wave function ψ(x) = ψ(0) = ...
I have provided solution to this problem without the use of tedious mathematical formula. Solution is very well presented with explanations.