Simple Harmonic Oscillator - Classical and Quantum Descriptions
SHO
Charles Hermite
French Mathematician
1822-1901
What do the following have in common?
Hydrogen
Nitrogen
Oxygen
Fluorine
Clorine
Bromine
Iodine
What do the following have in common?
Hydrogen
Nitrogen
Oxygen
Fluorine
Clorine
Bromine
Iodine
They all form diatomic molecules (H2 N2 O2 ……)
See extra credit problem on HW #8
PHGN 300 Homework #8 (6 problems + 1 extra credit)
6) The harmonic oscillator potential is U(x)=1/mω02x2; a particle of mass
m in this potential oscillates with frequency ω0. The ground-state
wavefunction for a particle in the harmonic oscillator potential has the
form ψ(x)=Aexp(-ax2)
By substituting (Ux) and ψ(x) into the one-dimensional timeindependent Schrodinger Equation, find expressions for the groundstate energy E and the constant a in terms of m, ħ, and ω0.
Extra Credit
The H2 molecule can be approximated by a simple harmonic oscillator
having spring constant k=1.1x103 N/m. Find (a) the energy levels and (b)
the possible wavelengths of photons emitted with the H2 molecule
decays from the third excited state eventually to the ground state.
http://phet.colorado.edu/en/simulation/bound-states