Delta function terms in a non-relativistic hyperfine calculation for the hydrogen atom
Keyword(s):
An inconsistency previously found between the relativistic and non-relativistic second-order hyperfine energies of the hydrogen atom with a point nucleus is ascribed to the neglect of delta function contributions in the non-relativistic calculation. Various relations involving point delta functions are developed. In particular, a novel representation of the commutator of partial differential operators acting on a homogeneous function of degree −n + 2 in n variables is given in terms of the point delta function. With the inclusion of the delta function terms, the non-relativistic point-nucleus result is shown to be consistent with the results of both relativistic point-nucleus and non-relativistic finite-nucleus calculations.
1983 ◽
Vol 8
(6)
◽
pp. 643-665
◽
1970 ◽
Vol 69
(1)
◽
pp. 77-84
2006 ◽
Vol 342
(8)
◽
pp. 579-584
◽
Keyword(s):
2013 ◽
Vol 17
(2)
◽
pp. 379-406
◽
2010 ◽
Vol 365
(1)
◽
pp. 363-375
◽
1978 ◽
Vol 79
(3-4)
◽
pp. 193-226
◽
1973 ◽
Vol 73
(1)
◽
pp. 87-109
◽