Bound State Solutions of the Relativistic Finite-difference Equation for the Ring-shaped Quesne Oscillator Potential

• URL: http://arxiv.org/abs/2606.12082v1
• Date: Wed, 10 Jun 2026 13:46:30 GMT
• Title: Bound State Solutions of the Relativistic Finite-difference Equation for the Ring-shaped Quesne Oscillator Potential
• Abstract summary: We solve exactly the relativistic finite-difference equation for the quantum three-dimensional ring-shaped Quesne oscillator potential.<n>Our investigation is based on a finite-difference version of relativistic quantum mechanics.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We solve exactly the relativistic finite-difference equation for the quantum three-dimensional ring-shaped Quesne oscillator potential. Our investigation is based on a finite-difference version of relativistic quantum mechanics. So-called relativistic configurational r-space is a key concept here. We show that the radial wavefunctions and angular wavefunctions are expressed through the continuous dual Hahn polynomials and Jacobi polynomials, respectively. A discrete energy spectrum has been found. The radial wave functions and energy spectrum have the correct nonrelativistic limit. We also build a dynamical symmetry group SU (1, 1) for the radial part of the equation of motion, which allows us to find the energy spectrum purely algebraically.

Related papers

• A generalized harmonic oscillator problem for a spin-1/2 fermion [0.0]
  The exact bound-state solutions are computed by tuning coefficients for an appropriate pair of textitAnstze for the radial functions.<n>Although the energy equation cannot provide a general expression for the energy spectrum, specific constraints on the quantum numbers parameters can be derived.
  arXiv  Detail & Related papers  (2026-09-02T03:17:44Z)
• Relativistic bound-state solutions for a non-central Schi{ö}berg-type hyperbolic potential with double ring-shaped angular terms [0.0]
  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.
  arXiv  Detail & Related papers  (2026-07-02T12:52:18Z)
• Unitary Time Evolution and Vacuum for a Quantum Stable Ghost [36.94429692322632]
  We prove that due to an integral of motion with a positive discrete spectrum the Hamiltonian has a pure point spectrum unbounded in both directions.<n>We argue that the discrete spectrum of the integral of motion enforces stability for extended interactions.
  arXiv  Detail & Related papers  (2026-04-23T16:15:51Z)
• Bound, antibound and resonance two-photon states in chiral waveguide QED [51.56484100374058]
  We present a theoretical study of the two-particle spectrum $(K)$ for the chiral waveguide QED setup.<n>For each pair center-of-mass momentum $K$ there exist distinct solutions with $Imle 0$ in the two-particle spectrum.<n>An interesting finding is that the real part of the spectrum $Re (K)$ in the chiral model is gapless.
  arXiv  Detail & Related papers  (2026-04-22T14:19:46Z)
• Schrödinger equation is $\mathcal{R}$-separable in toroidal coordinates [45.88028371034407]
  We present, for the first time, exact solutions for the Schrdinger equation in Moon and Spencer's toroidal coordinates.<n>We achieve these novel solutions using the irregular $mathcalR$-separation of variables.
  arXiv  Detail & Related papers  (2025-11-10T21:12:13Z)
• Revivals and quantum carpets for the relativistic Schrödinger equation [41.99844472131922]
  We investigate wavepacket dynamics for a relativistic particle in a box evolving according to the Schr"odinger equation.<n>We obtain expressions for the wavepacket revival times and explore the corresponding quantum carpets.<n>We analyze level spacing statistics as the dynamics goes from the non-relativistic regime to the ultra-relativistic limit.
  arXiv  Detail & Related papers  (2025-11-07T12:39:00Z)
• A pseudo-random and non-point Nelson-style process [49.1574468325115]
  We take up the idea of Nelson's processes, the aim of which was to deduce Schr"odinger's equation.<n>We consider deterministic processes which are pseudo-random but which have the same characteristics as Nelson's processes.
  arXiv  Detail & Related papers  (2025-04-29T16:18:51Z)
• Employing an operator form of the Rodrigues formula to calculate wavefunctions without differential equations [0.0]
  The factorization method of Schrodinger shows us how to determine the energy eigenstates without needing to determine the wavefunctions in position or momentum space. This approach can be used in either undergraduate or graduate classes in quantum mechanics.
  arXiv  Detail & Related papers  (2023-12-14T20:21:17Z)
• Energetics of the dissipative quantum oscillator [22.76327908349951]
  We discuss some aspects of the energetics of a quantum Brownian particle placed in a harmonic trap. Based on the fluctuation-dissipation theorem, we analyze two distinct notions of thermally-averaged energy. We generalize our analysis to the case of the three-dimensional dissipative magneto-oscillator.
  arXiv  Detail & Related papers  (2023-10-05T15:18:56Z)
• Quantum model of hydrogen-like atoms in hilbert space by introducing the creation and annihilation operators [0.0]
  An analytical approach with series is extensively used based on wave mechanics theory in most of quantum textbooks. We will illustrate how systematically making an appropriate groundwork to discover the coherent states can lead to providing the energy quantization and normalized radial wave functions attached to the matrix representation.
  arXiv  Detail & Related papers  (2023-08-25T14:42:55Z)
• Double-scale theory [77.34726150561087]
  We present a new interpretation of quantum mechanics, called the double-scale theory. It is based on the simultaneous existence of two wave functions in the laboratory reference frame. The external wave function corresponds to a field that pilots the center-of-mass of the quantum system. The internal wave function corresponds to the interpretation proposed by Edwin Schr"odinger.
  arXiv  Detail & Related papers  (2023-05-29T14:28:31Z)
• The Half Transform Ansatz: Quarkonium Dynamics in Quantum Phase Space [0.0]
  We present a method to cast the Schrodinger Equation into a hyper-geometric form which can be solved for the phase space wave function and its energy eigenvalues. We also analyze the behavior of these wave functions, which suggest a correlation between radial momentum and the upper limit of existence in charm-anticharm mesons.
  arXiv  Detail & Related papers  (2023-03-28T23:38:57Z)
• Approximate Solutions to the Klein-Fock-Gordon Equation for the sum of Coulomb and Ring-Shaped like potentials [0.0]
  We consider the quantum mechanical problem of the motion of a spinless charged relativistic particle with mass$M$. It is shown that the system under consideration has both a discrete at $left|Eright|Mc2 $ and a continuous at $left|Eright|>Mc2 $ energy spectra. It is also shown that relativistic expressions for wave functions, energy spectra and group generators in the limit $ctoinfty $ go over into the corresponding expressions for the nonrelativistic problem.
  arXiv  Detail & Related papers  (2020-04-27T08:49:10Z)
• External and internal wave functions: de Broglie's double-solution theory? [77.34726150561087]
  We propose an interpretative framework for quantum mechanics corresponding to the specifications of Louis de Broglie's double-solution theory. The principle is to decompose the evolution of a quantum system into two wave functions. For Schr"odinger, the particles are extended and the square of the module of the (internal) wave function of an electron corresponds to the density of its charge in space.
  arXiv  Detail & Related papers  (2020-01-13T13:41:24Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.