A particle of mass m near the earth’s surface at z = 0 can be described by the potential energy

U = mgz, z > 0

U = ∞, z < 0

For some positive value of total energy E, indicate the classically allowed region on a sketch of U(z) versus z. Sketch also the classical kinetic energy versus z. The Schrödinger equation for this problem is quite difficult to solve. Using arguments similar to those in Section 36-2 about the curvature of the wave function as given by the Schrödinger equation, sketch your "guesses" for the shape of the wave function for the ground state and the first two excited states.