# Near Normalization calculation for given wavefunction

1. Sep 11, 2007

### JamesJames

Near "Normalization" calculation for given wavefunction

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

A wave function is given by Y(E) = CEexp(-E/kt)

1. Find C so that Y(E) becomes Y0 where Y0 is a constant.

2. Calculate the mean energy with respect to Y(E).

3. Find Y(t) as a function of wavelength and calculate the mean wavelength.

3. The attempt at a solution

1. Ok, I'm a bit conufsed by this "normalization" concept as it applies here. I understand normalization requiring Y*Y = 1 etc. but that would require the outcome to be 1. Here, the outcome is a constant. I could just say

$$\int_{-\infty}^{\infty}Y\left(t\right)Y^*\left(t\right)dt=1$$

but the "Y0" part is throwing me off.

2. Shouldn't it just be

<E> = $$\int_{-\infty}^{\infty}Y\left(t\right)EY^*\left(t\right)dt$$

where the exponentialterms would cancel leaving E and other constants? I would presumably calculate this AFTER having solved for C above.

3. I will get to this a bit later and post my attempt here a little later.

Last edited: Sep 11, 2007