Aone-dimensional particle of mass m is confined within the region
0 ≤ x ≤ a and wave function ψ(x, t) = sin( πx a )e −iωt .
a by substituting the wave function ψ(x, t) into the time-dependent schr¨odinger equation show that v is independent of t.
b calculate the probability of finding the particle in the interval a 4 ≤ x ≤ 3a 4 .