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JamesJames
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Near "Normalization" calculation for given wavefunction
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.
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
[tex]\int_{-\infty}^{\infty}Y\left(t\right)Y^*\left(t\right)dt=1[/tex]
but the "Y0" part is throwing me off.
2. Shouldn't it just be
<E> = [tex]\int_{-\infty}^{\infty}Y\left(t\right)EY^*\left(t\right)dt [/tex]
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.
Homework Statement
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.
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
[tex]\int_{-\infty}^{\infty}Y\left(t\right)Y^*\left(t\right)dt=1[/tex]
but the "Y0" part is throwing me off.
2. Shouldn't it just be
<E> = [tex]\int_{-\infty}^{\infty}Y\left(t\right)EY^*\left(t\right)dt [/tex]
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.
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