Find the only way to construct a length from the parameters in the Schrodinger equation for the harmonic oscillator.

(a) Find the only way to construct a length from the parameters in the Schrodinger equation for the harmonic oscillator. Compare the result with the classical amplitude of oscillation when the energy is hw/2.

where h=h-bar

(b) Find the only way to construct a length from the parameters in the Schrodinger equation for the hydrogen atom. Compare with the Bohr radius.

(c) How would you expect the characteristic length of each system to vary with its quantum number n?