Question

Consider a system in a one-dimensional box in an energy state n=3.

a) Determine the locations of the maximum probability if the box goes from x=0 to x=L. There may be more than one such point.

b) Calculate the probability the particle is found between x=0 and the value of x one half the distance to the (first) probability maximum.

c) Repeat this calculation for the distance one half the way to the first probability maximum to the first probability maximum.

d) How many segments are there in the box that have the same probability as that calculated in b? Draw a picture of the probability distribution for n=3 and shade in these segments.