The harmonic oscillator potential energy is proportional to x2, and the energy levels are...

The harmonic oscillator potential energy is proportional to x2, and the energy levels are equally spaced: En ∞ (n + ½). The energy levels in the infinite well become farther apart as energy increases: En ∞ n2. Because the function lim→∞|x/L|b is 0 for |x|<L and infinitely large for |,x| > L, the infinite well potential energy may be thought of as proportional to |x|∞.

How would you expect energy levels to be spaced in a potential well that is (a) proportional to |x|1 and (b) proportional to -|x|-1 ? For the harmonic oscillator and infinite well, die number of bound-state energies is infinite, and arbitrarily large bound-state energies are possible.Arc these characteristics shared (c) by the |x|1 well and (d) by the -|x|-l well?

Exercises 78-88 refer to a particle of mass m described by the wave function