Wavefunctions and probability-Proof

[quantumech]

Prove that the probability of finding a particle of mass m in a one-dimensional potential well of length L is 0.5 for both the first and second half of the well for the state with n = 2. Demonstrate that these results make sense in light of the form of the wavefunction for each case.

Someone please help me with proofs. What is general outline i should follow to do this?

 

[buffordboy23]

Do you know the wave function for your potential well?

If so, compute the probability of finding the particle in (0,L/2) and then (L/2,0). You should find that the probabilities are equal.

Then plot $$\psi\left(x\right)$$ and $$\psi^{2}\left(x\right)$$. It should be apparent then.

 

[quantumech]

can I use the normalized particle in a box wavefunction, or should I normalize the constant in another manner.