摘要
This paper illustrates how homogeneous function analysis can be generalized. to relativistic quantum mechanics for finding the WKB energy levels of Dirac particle in the positive power-law potentials (V = lambda-r(v), S = lambda'r(v), lambda, lambda', v > 0). The results show that the equation determining energy levels contains a product of hypergeometric function with some gamma functions, and the energy of particle is proportional to (2n(r) + l + 3/2) 2v/1 + v under the condition that the relativistic effect plays a principal role in contrast with the (2n(r) + l + 3/2) 2v/2 + v dependence in nonrelativistic case.
This paper illustrates how homogeneous function analysis can be generalized. to relativistic quantum mechanics for finding the WKB energy levels of Dirac particle in the positive power-law potentials (V = lambda-r(v), S = lambda'r(v), lambda, lambda', v > 0). The results show that the equation determining energy levels contains a product of hypergeometric function with some gamma functions, and the energy of particle is proportional to (2n(r) + l + 3/2) 2v/1 + v under the condition that the relativistic effect plays a principal role in contrast with the (2n(r) + l + 3/2) 2v/2 + v dependence in nonrelativistic case.
