301 research outputs found
Comment on the orthogonality of the Macdonald functions of imaginary order
Recently, Yakubovich [Opuscula Math. 26 (2006) 161--172] and Passian et al.
[J. Math. Anal. Appl. doi:10.1016/j.jmaa.2009.06.067] have presented
alternative proofs of an orthogonality relation obeyed by the Macdonald
functions of imaginary order. In this note, we show that the validity of that
relation may be also proved in a simpler way by applying a technique
occasionally used in mathematical physics to normalize scattering wave
functions to the Dirac delta distribution.Comment: LaTeX, 4 page
Recurrence and differential relations for spherical spinors
We present a comprehensive table of recurrence and differential relations
obeyed by spin one-half spherical spinors (spinor spherical harmonics)
used in relativistic atomic, molecular, and
solid state physics, as well as in relativistic quantum chemistry. First, we
list finite expansions in the spherical spinor basis of the expressions
and
{}, where , , and
are either of the following vectors or vector operators:
(the radial unit vector), ,
(the spherical, or cyclic, versors),
(the Pauli matrix vector),
(the dimensionless
orbital angular momentum operator; is the unit matrix),
(the dimensionless
total angular momentum operator). Then, we list finite expansions in the
spherical spinor basis of the expressions
and
, where at least one of the objects
, , is the nabla operator
, while the remaining ones are chosen from the set
, , , ,
, .Comment: LaTeX, 12 page
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