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Unformatted text preview: Problem Set 7.
(Adapted from Jackson 9.10) The transitional charge and current densities for the radiative transition from the m 0, 2p state in hydrogen to the 1s ground state are (with the neglect of spin), r, , , t 2e 4 r exp 3r Y 00 Y 10 expi o t; 2a o 6 ao Jr, , , t iv o r a o zr, , , t. z 22 where a o 4 o 2 /me 2 0. 529 10 10 m is the Bohr radius, o 3e 2 /32 o a o is the frequency difference of the levels, and v o e 2 /4 o c c/137 is the Bohr orbit speed. a) Find the general expression for the vector potential, Ar, t, and the r, t for this localized radiation source. b) Evaluate all the nonvanishing radiation multipole contributions in the long wavelength limit. c) Find the magnetic induction, Br, t, and the electric field, Er, t, in the radiation limit. ...
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