(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A Hydrogen atom in its ground state (n,l,m) = (1,0,0) is placed in a weak electric field

E(t) = 0 if t < 0

[tex]Eo *e^{\frac{-t}{\tau}} [/tex]if t > 0

E is in the positive z direction

What is the probability that it will be found in any of the n=2 states at time t > 0 ? use first order perturbation theory

2. Relevant equations

[tex]C^{(1)}_{ba} = \frac{1}{(i\hbar)} \int^t_0 H'_{ba} e^{iw_{ba}t'}dt' [/tex]

where [tex] H'_{ba}[/tex] is the (b,a) matrix element of the perturbation and [tex]w_{ba} = \frac{(E^{(0)}_b - E^{(0)}_a)}{\hbar} [/tex]

3. The attempt at a solution

so basically i set up the schrodinger equation in spherical coordinates and added the perturbation [tex]H' = e*Eo *e^{\frac{-t}{\tau}}*rcos{\theta} [/tex]

where e is the magnitude of the charge charge of an electron. i then evaluated [tex]C_{ba} [/tex] for a = 1s and b = 2s, 2p0, 2p1, 2p-1 all separately.

i got [tex] H'_{ba} = 0 [/tex] for everything except 2p0, so the coefficients will be 0, for 2p0 i got this for the coefficient:

[tex] (\frac{e*Eo}{i\hbar3\sqrt{2}a^4_{\mu}})(\int^{\infty}_0 r^4 e^{\frac{-3r}{2a_{\mu}}}dr)(\frac{1}{\frac{i3\mu e^4}{128\pi^2 \epsilon^2_o\hbar^3} - \frac{1}{\tau}})(e^{t(\frac{i3\mu e^4}{128\pi^2\epsilon^2_0\hbar^3}-\frac{1}{\tau}]}-1) [/tex]

[tex]

a_{\mu} =\frac{4\pi\epsilon_o\hbar^2}{\mu e^2}

[/tex]

[tex]

\mu = [/tex] reduced mass

and then just take the absolute value squared to get the probability of being found in that state at time t. i was wondering if i did this right? also sorry about using e for the exponential and the charge, if it has variables in its power then its the exponential, otherwise its charge.

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# Homework Help: Time-dependent perturbation theory: hydrogen atom in electric field

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