Consider a particle confined to a cube of side a Calculate t

Consider a particle confined to a cube of side a. Calculate the probability that the particle in its ground state is found in the subcube given by: 3a y345z1s 313 4 4 4 4 4 4

Solution

volume of the cube with side a is a³

now the sides of the subcube defined by the given conditions will be 3a/4 - a/4 = a/2

so the volume of the subcube is (a/2)³ = a³/8

probability = (volume of subcube)/(volume of the cube)

p = (a³/8)/a³

p = 1/8

so the probability is 1/8 or 1/8*100% = 12.5%

so the probability that the particle in the subcube is 12.5%