quantum mechanics 5

1. A ball of mass m feels a uniform gravitational field (let g be the acceleration of gravity). The ball hits the floor elastically. Take the floor as a potential energy benchmark equal to zero and write the Schrödinger equation as an Airy equation and use conditions of frontier to determine energy levels.

2. Consider a particle in the nth stationary state of the one-dimensional harmonic oscillator of frequency w.

a) Find the return point as a function of energy.

b) How much can you move above the return point before the error in the

linearization of the potential reaches 1%.