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1. The problem statement, all variables and given/known data
See attached. The problem is labeled "Peatross 1". Don't worry, it's short. I just didn't feel like retyping it.
2. Relevant equations
Included in attempt.
3. The attempt at a solution
I'm not sure if I am doing this correctly, but here it goes.
I'll just do it for [tex]H'_{10}[/tex], since the method will be the same for both.
I think all I have to do is calculate [tex]\psi_0[/tex] and [tex]\psi_1[/tex] using the following formula (for a harmonic oscillator):
[tex]\left\langle x  \psi_n \right\rangle = \sqrt{\frac{1}{2^n\,n!}} \cdot \left(\frac{m\omega}{\pi \hbar}\right)^{1/4} \cdot \exp
\left( \frac{m\omega x^2}{2 \hbar} \right) \cdot H_n\left(\sqrt{\frac{m\omega}{\hbar}} x \right)[/tex]
Then just compute the resulting integral (probably in Mathematica):
[tex]\int_{ \infty}^{\infty} \psi_0 exE_0 \sin{\omega_L t\psi_1^*} dx[/tex]
Is this all there is to it, or am I missing something?
Thanks for your help!
See attached. The problem is labeled "Peatross 1". Don't worry, it's short. I just didn't feel like retyping it.
2. Relevant equations
Included in attempt.
3. The attempt at a solution
I'm not sure if I am doing this correctly, but here it goes.
I'll just do it for [tex]H'_{10}[/tex], since the method will be the same for both.
I think all I have to do is calculate [tex]\psi_0[/tex] and [tex]\psi_1[/tex] using the following formula (for a harmonic oscillator):
[tex]\left\langle x  \psi_n \right\rangle = \sqrt{\frac{1}{2^n\,n!}} \cdot \left(\frac{m\omega}{\pi \hbar}\right)^{1/4} \cdot \exp
\left( \frac{m\omega x^2}{2 \hbar} \right) \cdot H_n\left(\sqrt{\frac{m\omega}{\hbar}} x \right)[/tex]
Then just compute the resulting integral (probably in Mathematica):
[tex]\int_{ \infty}^{\infty} \psi_0 exE_0 \sin{\omega_L t\psi_1^*} dx[/tex]
Is this all there is to it, or am I missing something?
Thanks for your help!
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