1-D Quantum Mechanics

A basic model of a hydrogen atom is a finite potential well with rectangular edges. A more realstic model of a hydrogen atom, although still a 1-Dimensional model, would be the electron + proton potential enrgy in one dimension:

U(x)  = -e^2/(4pi epsilon_0)|x|)

a) Draw a graph of U(x) versus x. Center your graph at x = 0.

b) Despite the divergence at x=  0, the Schrodinger Equation can be solved to find energy levels and wave functions for the electron in this potention. Draw a horizontal line across your graph of part a) about one-third the way from the bottom to the top. Label this line E2, the on this line, sketch a plausible graph of the  n = 2 wave function.

c) Redraw your graph of part a) and add a horizontal line about two-thirds the way from the bottom to the top. Label this line E_3, then, on this line, sketch a plausible graph of the  n = 3 wave function.