Dispersion relations for stark energy shifts in hydrogen atom |
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| Authors: | S C Kanavi C H Mehta S H Patil |
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| Institution: | Department of Physics, Indian Institute of Technology, Bombay-400 076, India;Mathematics Group, R and D Division, Institute for Petroleum Exploration, ONGC, Dehradun 248195, India;Department of Physics, Indian Institute of Technology, Bombay-400 076, India |
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| Abstract: | On the basis of an approximate but nonperturbative expression for the energy shift δE in the ground state of the hydrogen atom in the presence of an electric field of strength
, we deduce that δE has a branch point at
= 0, and an asymptotic behavior
ln
as
→ ∞. These properties lead to a twice-subtracted dispersion relation for δE as a function of
. The dispersion relations in conjunction with the WKB approximation and the perturbation series allow us to (i) deduce the large-n behavior of the coefficient of
n in the perturbation series for δE(
) including 1/n corrections and (ii) obtain the energy shift and the level width of the ground state for a large range of values of
. The agreement with the earlier numerical calculations is very satisfactory. |
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| Keywords: | |
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