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 SchrÃ¶dinger 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%.
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