Probabilty of Particle in Box Between 0.4a and 0.6a: Solution Attempt

[kasse]

Homework Statement

A particle is trapped in an infinite one-dimensional square well which extends between x=0 and x=a. If the particle is in the ground state, calculate the probability that it is between 0.4a and 0.6a.

2. The attempt at a solution

The normalised of the ground state is sqrt((2/a)sin(pi*x/a)

Setting k = pi/a, I get the probability

(2/a)Int(sin^2(kx)dx for 0.4 - 0.6. How can I solve this integral?

 

[George Jones]

If you've taken first-year integral calculus, you have seen this type of integral. Do you know any trig identities that involve sin^2 \theta?

 

[shanu_bhaiya]

sin²x = (1-cos2x)/2 and then integrate.

May be someone said that:
"Physics is too tough for Physicists."
... may be he was Schrödinger.