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?
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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.
Hamiltonian operator and calculation of force
1] Write down the Hamiltonian operator for the following problems:
a. Particle in a box (of length L)
b. Free Particle
c. Harmonic oscillator
2] In the infrared spectrum of H79Br there is an intense line at 2.60 X 10^3 cm^-1. Calculate the force constant of H^79Br and the period of vibration.View Full Posting Details