An Introduction to Special Functions with Some Applications to Quantum Mechanics

Discovery of the Relativistic Schrödinger Equation

“…One can see that it's a bit harder than the corresponding nonrelativistic case originally published in Ref. [30] (see also [1], [21], [28], [34] for modern treatments).…”

“…where j = 1/2, 3/2, 5/2, ... is the total angular momentum including the spin of the relativistic electron. A detailed solution of this problem, including the nonrelativistic limit, can be found in [28], [34] (in Nikiforov-Uvarov's paradigm), or in classical sources [1], [9], [15], [29].…”

“…In Dirac's theory of the relativistic electron, the corresponding limit has the form [1], [9], [29], [34]:…”

“…where a 0 = 2 /me 2 is Bohr's radius. As a result, from (3.23)-(3.24) one gets the nonrelativistic radial wavefunctions of the hydrogenlike atom [1], [21], [30], [34]:…”

“…In Table 1, provided in Appendix A, we present the corresponding data for the nonrelativistic hydrogenlike atom for the reader's convenience. (More details can be found in [28], [34]. )…”