Physics · Quantum Mechanics

Consider the quantum mechanical analog to the classical problem of a ball of mass m bouncing elastically on the floor under gravity g ẑ. For negative z, the potential energy is infinity. The energy eigenvalues En can be found by the W.K.B. approximation. If En3 = α(n - 14)2 π2 ℏ2 g, where n = 1, 2, 3, ..., then the value of α is: