Question

Exercise 40.48 from Young/Freedman, University Physics with Modern Physics, 14e

Consider a particle in a box with rigid walls at x=0 and x=L. Let the particle be in the ground level.

Part A

Calculate the probability |ψ|2dx that the particle will be found in the interval x to x+dx for x=L/4.

(Express your answer in terms of the variables dx and L.)

Part B

Calculate the probability |ψ|2dx that the particle will be found in the interval x to x+dx for x=L/2.

(Express your answer in terms of the variables dx and L.)

Part C

Calculate the probability |ψ|2dx that the particle will be found in the interval x to x+dx for x=3L/4.

(Express your answer in terms of the variables dx and L.)

Answer 1

The ground state wave function is given by
   
And so,
  

Part - A :
The probability that the particle will be found in the interval   to   
  
  
  

Part - B :

The probability that the particle will be found in the interval   to   
  
  
  

Part - C :

    The probability that the particle will be found in the interval   to