Abstract:
A mathematical procedure is given for investigating the regular degeneration of the solutions
of the relativistic Schrödinger equation
$$
[2c\sqrt{q^2+m^2c^2}-H_0^{\operatorname{rad}}-V(r)]\Psi_{ql}(r)=0
$$
into the solutions of the nonrelativlstle equation
$$
\left[\hbar^2\frac{d^2}{dr^2}-\hbar^2\frac{l(l+1)}{r^2}-mV(r)+q^2\right]u_{ql}(r)=0
$$
for the $S$-wave case. The proposed method of a small parameter of the higher derivatives
of a differential equation is applied to several concrete problems.