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Safder Aree

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## Homework Statement

I have the wave function Ae^(ikx)*cos(pix/L) defined at -L/2 <= x <= L/2. and 0 for all other x.

The question is:

A proton is in a time-independent one-dimensional potential well.What is the probability that the proton is located between x = − L/4 and x = L/4 ?

## Homework Equations

∫ψψ* = 1

## The Attempt at a Solution

I know i have to normalize this first. Should I be normalizing with the bounds being -L/2 and L/2 or should the bounds be -L/4 and L/4.

A^2∫cos^2(πx/L)dx =1

(1/2)A^2[x+ L/2π (sin(2πx/L)] evaluated at some bounds.

I actually evaluated it both ways one answer gives me A=√2/L at L/2,-L/2 and the other one gives me A = √2

π/L which makes more sense (at -L/4,L/4)

But i just want to make sure i am approaching this right way.

Thank you.

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