Three-Dimensional Eigenvalues of Harmonic Oscillator- and Coulomb-type Potentials from One-Dimensional Generalized Morse Potential: Perturbative Analyse based on Generalized Laguerre Polynomials

• URL: http://arxiv.org/abs/2311.07917v1
• Date: Tue, 14 Nov 2023 05:30:33 GMT
• Title: Three-Dimensional Eigenvalues of Harmonic Oscillator- and Coulomb-type Potentials from One-Dimensional Generalized Morse Potential: Perturbative Analyse based on Generalized Laguerre Polynomials
• Authors: Altug Arda
• Abstract summary: We present perturbative energy eigenvalues (up to second order) of Coulomb- and harmonic oscillator-type fields within a perturbation scheme. We have the required unperturbed eigenvalues ($E_n(0)$) analytically obtained by using similarities between the expressions obtained from unperturbed Hamiltonian(s) for two fields and obtained from the ones for one-dimensional generalized Morse field.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present perturbative energy eigenvalues (up to second order) of Coulomb- and harmonic oscillator-type fields within a perturbation scheme. We have the required unperturbed eigenvalues ($E_{n}^{(0)}$) analytically obtained by using similarities between the expressions obtained from unperturbed Hamiltonian(s) for two fields and obtained from the ones for one-dimensional generalized Morse field. We use the Langer transformation for this aim. We need the diagonal and non-diagonal matrix elements of unperturbed and perturbed Hamiltonians to get energy eigenvalues perturbatively, which are obtained with help of some recursion identities or some integrals of generalized Laguerre polynomials having analytical results.

Related papers

• Chiral Virasoro algebra from a single wavefunction [14.735587711294299]
  When the edge is purely chiral, the Hilbert space of low-energy edge excitations can form a representation of a single Virasoro algebra. We propose a method to systematically extract the generators of the Virasoro algebra from a single ground state wavefunction.
  arXiv  Detail & Related papers  (2024-03-27T09:54:21Z)
• Imaginary eigenvalues of Hermitian Hamiltonian with an inverted potential well and transition to the real spectrum at exceptional point by a non-Hermitian interaction [0.6144680854063939]
  The Hermitian Hamiltonian can possess imaginary eigenvalues in contrast with the common belief that hermiticity is a suffcient condition for real spectrum. The classical counterpart of the quantum Hamiltonian with non-Hermitian interaction is a complex function of canonical variables. It becomes by the canonical transformation of variables a real function indicating exactly the one to one quantum-classical correspondence of Hamiltonians.
  arXiv  Detail & Related papers  (2024-02-09T02:58:06Z)
• Improving Expressive Power of Spectral Graph Neural Networks with Eigenvalue Correction [55.57072563835959]
  spectral graph neural networks are characterized by filters. We propose an eigenvalue correction strategy that can free filters from the constraints of repeated eigenvalue inputs.
  arXiv  Detail & Related papers  (2024-01-28T08:12:00Z)
• Harmonic Oscillator with a Step and its Isospectral Properties [0.0]
  We investigate the one-dimensional Schr"odinger equation for a harmonic oscillator with a finite jump $a$ at the origin. The solution is constructed by employing the ordinary matching-of-waves technique.
  arXiv  Detail & Related papers  (2023-07-26T15:31:31Z)
• Solutions of (1+1)-dimensional Dirac equation associated with exceptional orthogonal polynomials and the parametric symmetry [7.343280016515051]
  We consider $1+1$-dimensional Dirac equation with rationally extended scalar potentials corresponding to the radial oscillator, the trigonometric Scarf and the hyperbolic Poschl-Teller potentials.
  arXiv  Detail & Related papers  (2022-11-04T16:23:05Z)
• Theory for Coulomb scattering of trions in 2D materials [19.444636864515726]
  We develop a theoretical description of Coulomb interactions between trions (charged excitons) that define a nonlinear optical response in doped two-dimensional semiconductors. We find that the considered scattering gives significant contribution to the optical nonlinearity in monolayers of transition metal dichalcogenides.
  arXiv  Detail & Related papers  (2022-07-06T13:27:40Z)
• An ubiquitous three-term recurrence relation [0.0]
  We solve an eigenvalue equation that appears in several papers about a wide range of physical problems. We compare the resulting eigenvalues with those provided by the truncation condition. In this way we prove that those physical predictions are merely artifacts of the truncation condition.
  arXiv  Detail & Related papers  (2021-10-25T20:00:31Z)
• When can a local Hamiltonian be recovered from a steady state? [11.031662961887243]
  Hamiltonians of two spin chains with 2-local interactions and 3-local interactions can be recovered by measuring local observables. We show that when the chain length reaches a certain critical number, we can recover the local Hamiltonian from its one steady state by solving the homogeneous operator equation (HOE) To explain the existence of such a critical chain length, we develop an alternative method to recover Hamiltonian by solving the energy eigenvalue equations (EEE)
  arXiv  Detail & Related papers  (2021-09-16T02:37:17Z)
• Intrinsic decoherence dynamics in the three-coupled harmonic oscillators interaction [77.34726150561087]
  We give an explicit solution for the complete equation, i.e., beyond the usual second order approximation used to arrive to the Lindblad form.
  arXiv  Detail & Related papers  (2021-08-01T02:36:23Z)
• On some conditionally solvable quantum-mechanical problems [0.0]
  We show diagrams of the distribution of their exact eigenvalues with the addition of accurate ones from variational calculations. We also comment on the wrong interpretation of the exact eigenvalues and eigenfunctions by some researchers that has led to the prediction of allowed cyclotron frequencies and field intensities.
  arXiv  Detail & Related papers  (2020-07-07T13:55:00Z)
• Hartmann potential with a minimal length and generalized recurrence relations for matrix elements [0.0]
  We study the Schr"odinger equation in the presence of the Hartmann potential with a generalized uncertainty principle. We pertubatively obtain the matrix elements of the hamiltonian at first order in the parameter deformation of $beta$ and show that some degenerate states are removed.
  arXiv  Detail & Related papers  (2020-02-09T11:40:03Z)

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.