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- Title
The second Exton potential for the Schrödinger equation.
- Authors
Ishkhanyan, Artur M.; Karwowski, Jacek
- Abstract
Analytical solutions of the Schrödinger equation with a singular, fractional-power potential, referred to as the second Exton potential, are derived and analyzed. The potential is defined on the positive half-axis and supports an infinite number of bound states. It is conditionally integrable and belongs to a biconfluent Heun family. The fundamental solutions are expressed as irreducible linear combinations of two Hermite functions of a scaled and shifted argument. The energy quantization condition results from the boundary condition imposed at the origin. For the exact eigenvalues, which are solutions of a transcendental equation involving two Hermite functions, highly accurate approximation by simple closed-form expressions is derived. The potential is a good candidate for the description of quark–antiquark interaction.
- Subjects
QUARK confinement; SCHRODINGER equation; BOUND states; ANALYTICAL solutions
- Publication
Modern Physics Letters A, 2019, Vol 34, Issue 24, pN.PAG
- ISSN
0217-7323
- Publication type
Article
- DOI
10.1142/S0217732319501955