Particle in a box

[roshan2004]

1. The problem statement, all variables and given/known data

A particle is moving in a one dimensional box of infinite height of width 10 Angstroms. Calculate the probability of finding the particle within an interval of 1 Angstrom at the centre of the box, when it is in its state of least energy.

2. Relevant equations


\psi _{n}=\sqrt{\frac{2}{L}}sin \frac{n\pi x}{L}


3. The attempt at a solution
The wave function of the particle in the ground state (n=1) is \psi _{1}=\sqrt{\frac{2}{L}}sin \frac{\pi x}{L}. Now, what should I do ?

[Feldoh]

How does one find the probability amplitude in QM?

[roshan2004]

Square of its wavefunction. I got <tex> \frac{2}{L}sin^2 \frac{\pi x}{L}</tex> Now...........

[Feldoh]

Okay, now how do you find the probability on the interval [4 Angstroms,6 Angstroms]?

[roshan2004]

Why between 4 and 6 angstroms ?

[Feldoh]

Why do you think it's between 4 and 6 angstroms?

EDIT: Err rather I believe it should be from 4.5 to 5.5 angstroms...

[graphene]

probability of finding the particle between x & x+dx is {|\Psi|}^{2}

probability of finding the particle between x=a and a=b is \int_{a}^{b}{|\Psi|}^{2}dx

[roshan2004]

What are the limits I should use for the integration?

[graphene]

Find a and b for "an interval of 1 Angstrom at the centre of the box".