Need help with Physical Electronics course assignment.

**1-dim classical harmonic oscillator with spring constant****k**

Give the classical Hamilton, which is sum of the kinetic and potential energy.

Calculate the speed of the attached particle as a function of distance from the balance point.

Plot x-dependences of total energy, kinetic energy, potential energy, and speed

**1-dim quantum harmonic oscillator**

Give the quantum mechanical Hamiltonian, and boundary condition

Give the total energy dependence on quantum number

Give the general form of the wavefunctions

Plot the first three wave functions

**Higher dimensional quantum harmonic oscillator**

Go through the procedure of solving 2-dim quantum oscillator using separation of variable methods

Give the energy solutions and wavefunctions

Repeat solution for 3-dim case

**Electronics analogy**

Give an example from electronics circuits of harmonic oscillation

Calculate the equivalent classical spring constant, oscillation frequency, and total stored energy

Calculate the quantum mechanical energy levels and their separations

**Atom interaction potential**

Give the form of Lenard Jones potential

Calculate the balance point

Expand the potential around the balance point

Can we use harmonic oscillator to model near balance point potential?

If so, calculate the valid range. If not, demonstrate the reason