申論題

一、Physical Chemistry (5 questions of total 50 points)

(1, 12pts)

The one-dimensional quantum mechanical harmonic oscillator can be used to approximate the nature of vibrational motion of molecules. The harmonic oscillator model has the potential of V(x) =(1/2)kx², where x is the bond length and k is the force constant. Therefore, we should consider this to a mathematically equivalent problem as a single reduced mass u tethered to a wall of infinite mass of spring with a force constant k. The Schrodinger equation can be written as: 

(1A, 4pts) If is the eigenfunction ofthe above Schrodinger equation,what is B?