the wave functions for a particle in an infinite square well(between rigid walls) are described by: (x)=A sin(nπx/L) where n denotes the (quanitized) energy states of the particle and L is the width of the square well. Normalize the function , such that you determine the value for the arbitrary constant A. what is the probability to find the particle within x=(0,1/3) for the first three energy states (n=1,2,3)? From classical considerations , what would you think these probabilities should be?

Question

the wave functions for a particle in an infinite square well(between rigid walls) are described by: (x)=A sin(nπx/L)   where n denotes the (quanitized) energy states of the particle and  L is the width of the square well. Normalize the function , such that you determine the value for the arbitrary constant A. what is the probability to find the particle within x=(0,1/3) for the first three energy states (n=1,2,3)? From classical considerations , what would you think these probabilities should be?