Toy Problems for Fun

Interaction of Electrons in 2D

Schrodinger equation directly solved for 2 electrons in 2 dimensions held within a harmonic oscillator potential. NOTE: The Hamiltonian is H = KE + HARMONIC + C*Coulomb, where C is a paramter that can be used to slowly turn up the effect of the Coulomb potential.

We can also examine the dynamic behavior of what is initially a stationary state as we applying a time varying voltage to the harmonic well: