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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