Unformatted text preview: Problem set‐1. (Always works using atomic units and then convert to the regular units after the calculation.) 1. (a) Work out the wavefunctions of Stark states of hydrogen atom for n=4 and m=0. (b) Graph the density in (r,θ) plane or using the two parabolic coordinates. (c) Use first order perturbation theory to calculate the energy shift for each state in a static electric field of strength 104 V/cm. Express your results in eV. Explain if you are justified to use the perturbation theory. (hint: You can construct the Stark states using spherical coordinates or parabolic coordinates.) 2. Calculate the lifetime of the 2p state of atomic hydrogen and show that it is 1.6 ns. Without new calculations, what is the lifetime of the 2p state of He+. 3. For a two‐level atom, you can use the formulae from the so‐called Rabi oscillations to estimate the electric field you need to populate the excited state to almost 100%. (a) Estimate the intensity of the “laser” you need if the two levels are the 3s and 3p (take 3p1/2) of Na. (b) Estimate the intensity of the XUV “laser” you need if the two levels are the 1s and 2p states of atomic hydrogen. 4. Go to A. T. Le et al, Phys. Rev. A80, 013401 (2009), see Eq. (28). From there go through the derivation yourselves to show that his final result, Eq. (33) is correct (or not?). Read carefully that he considers the k‐vector in the direction of polarization only. ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ due 2/10 ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ ...
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- Spring '09
- Work, Perturbation theory, atomic hydrogen, Order Perturbation Theory, Stark states