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# Need help with Physical Electronics course assignment. 1-dim classical harmonic

Need help with Physical Electronics course assignment.

1. 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. 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

2. 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

3. 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

4. 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