The controls allow to change system parameters (the mass, linear and energy scale of the potential, energy) and explore dependency of wave-fuction of the system from energy, compare it with hamitltonian eigenfunctions.

Tools: AS1, FlaCon library

The Morse Potential

In this simulation, you will experimentally determine the allowed energy
levels for an anharmonic oscillator. Rather than using the harmonic potential
, the more realistic Morse potential

is used to model the potential. A comparison of the harmonic and anharmonic Morse
potentials is shown below.

Morse potential, V(x), (solid line) as a function of the bond length, x, for HCl,
using the parameters from Example Problem 8.3. The zero of energy is chosen to be
the bottom of the potential. The dashed curve shows a harmonic potential, which is
a good approximation to the Morse potential near the bottom of the well. The horizontal
lines indicate allowed energy levels in the Morse potential. D_{e} and
D_{0} are the bond energies defined with respect to the bottom of the
potential and the lowest state, respectively, and x_{e} is the equilibrium bond length.

The energy levels in the Morse potential are given by

Note from the figure that the energy spacing between adjacent energy
levels is not equal. You will determine the allowed energy levels in a Morse potential
by numerically integrating the Schrodinger equation, starting in the classically forbidden
region to the left of the potential. The criterion that the energy you chose is an energy
eigenvalue for the problem is that the wave function decays to zero in the classically
forbidden region to the right of the potential.

By experimentally finding the allowed energy levels in the potential how
many bound states there are in the Morse potential with
D_{e} = 9.00·10^{-29} J and
ν = 5.00·10^{13} s^{-1}.

b) How do the total energy eigenfunctions differ from those for the
harmonic potential?

c) What is the likelihood of finding the harmonic oscillator compressed
relative to being expanded? What is the likelihood of finding the Morse oscillator compressed
relative to being expanded?