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## Homework Statement

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Calculate the rate of ionization of a hydrogen atom in the 2p state in a monochromatic external electric field, averaged over the component of angular momentum in the direction of the field. Ignore the spin of the particles. In this case we can write:

[tex] H'(t)=-eEx_3exp(-i\omega t) -eE^*x_3exp(i\omega t)[/tex]

assuming that the electric field E is in the x

_{3}direction.

## Homework Equations

The 2p hydrogen wave function: [itex] \psi_{2p}=\frac{1}{2 \sqrt{6}a^{5/2}}re^{\frac{-r}{2a}} Y_1^m[/itex]

The wave function of a free particle: [itex] \psi_f=\frac{1}{(2 \pi a)^{3/2}} e^{ik \cdot x}[/itex]

## The Attempt at a Solution

I know the magnitude squared of the following relation will give me the probability of a transition:

[tex] \frac{dc_{2p}}{dt} = \frac{-i}{\hbar} H'_{(2p,e)}e^{-i \omega_0 t}c_f [/tex]

where [itex] \omega_0=\frac{E_f-E_{2p}}{\hbar}[/itex] and [itex] H'_{(2p,e)}= <\psi_{2p}|H'|\psi_f>[/itex].

My problem at this point is to set up the integral with the perturbed Hamiltonian and the two wave functions. I feel like I'm doing something wrong because I'm integrating with respect to x, but the 2p wave function is in terms of r. I don't know if I should be using a 3d version of the free particle or not.

Also, I'm not sure what is meant by "averaged over the component of angular momentum in the direction of the field" but it sounds like it's relevant to my first concern.

Finally, does "Ignore the spin of the particles" mean I can ignore the spherical harmonic portion of the 2p wave function? If not, how do I choose which value of m (-1, 0, 1) to use.

Thanks,

Any help would be appreciated.