Relativistic bound-state solutions for a non-central Schi{ö}berg-type hyperbolic potential with double ring-shaped angular terms

• URL: http://arxiv.org/abs/2607.16265v1
• Date: Thu, 02 Jul 2026 12:52:18 GMT
• Title: Relativistic bound-state solutions for a non-central Schi{ö}berg-type hyperbolic potential with double ring-shaped angular terms
• Abstract summary: We study the mechanism in the Klein--Gordon equation for a non-central Schiberg-type hyperbolic potential with double ring-shaped angular barriers.<n>We obtain Jacobi-polynomial wavefunctions and an implicit relativistic quantization condition.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Singular interactions can reshape quantum spectra by changing admissible wavefunction domains. In this study, we investigate this mechanism in the Klein--Gordon equation for a non-central Schiöberg-type hyperbolic potential with double ring-shaped angular barriers. Equal scalar and vector couplings separate the radial and angular dynamics. We solve the angular equation exactly and treat the radial equation with the Greene--Aldrich approximation, obtaining Jacobi-polynomial wavefunctions and an implicit relativistic quantization condition. The equatorial inverse-square singularity splits configuration space into reflection-related sectors with identical angular spectra. Reducing the barrier to zero within one sector retains only odd-parity states, unlike the regular full-domain problem, which restores both parities. The nonrelativistic limit recovers the Schr{ö}dinger spectrum. For NaH and Na$_2$, low-lying vibrational energies agree reasonably with experiment, whereas near-dissociation deviations reveal asymptotic limitations.

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