Answer to Question #60941 in Quantum Mechanics for Ngô Quốc Đạt

Question

The one-dimensional time-independent Schrödinger equation is
.
a/ A particle of mass m is contained in a one-dimensional box of width a. The potential energy U(x) is infinite at the walls of the box (x = 0 and x = a) and zero in between (0 < x < a).
Show that the solutions have the form: U(x)=Csin(n.pi.x/a) . Find the constant C.
b/ For the case n = 3, find the probability that the particle will be located in the region a/3 <x< 2a/3
.
c/ Sketch the wave-functions and the corresponding probability density distributions for the cases n = 1, 2 and 3.