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1705395 
Journal Article 
Exact solutions of Dirac and Schrodinger equations for a large class of power-law potentials at zero energy 
Alhaidari, AD 
2002 
Yes 
International Journal of Modern Physics A: Particles and Fields; Gravitation; Cosmology; Nuclear Physics
ISSN: 0217-751X 
17 
30 
4551-4566 
WOS:000179627400004 
We obtain exact solutions of Dirac equation for radial power-law relativistic potentials at rest mass energies. It turns out that these are the relativistic extension of a subclass of exact solutions of Schrodinger equation at zero energy carrying representations of SO(2, 1) Lie algebra. The latter are obtained by point canonical transformations of the exactly solvable problem of the three dimensional oscillator. The wave function solutions are written in terms of the confluent hypergeometric functions and almost always square integrable. For most cases these solutions support bound states at zero energy. Some exceptional unbounded states are normalizable for nonzero angular momentum. Using a generalized definition, degeneracy of the nonrelativistic states is demonstrated and the associated degenerate observable is defined. 
exact solutions; zero energy; Dirac equation; power-law potentials; point canonical transformations; so(2,1) algebra