Construction of potential functions associated with a given energy spectrum -- An inverse problem. II

• URL: http://arxiv.org/abs/2006.10787v1
• Date: Thu, 18 Jun 2020 18:04:29 GMT
• Title: Construction of potential functions associated with a given energy spectrum -- An inverse problem. II
• Authors: Abdulaziz D. Alhaidari and Houcine Aounallah
• Abstract summary: We obtain a class of potential functions associated with the Wilson and "Jacobi basis" Additional potential functions for exactly solvable problems that correspond to the same energy spectrum formula but for different energys and bases are found.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We continue our solution of the inverse problem started by the first author in [Int. J. Mod. Phys. A 35, xxxx (2020), in production]. Additional potential functions for exactly solvable problems that correspond to the same energy spectrum formula but for different energy polynomials and bases are found. In this work, we obtain a class of potential functions associated with the Wilson polynomial and "Jacobi basis".

Related papers

• Cavity QED materials: Comparison and validation of two linear response theories at arbitrary light-matter coupling strengths [41.94295877935867]
  We develop a linear response theory for materials collectively coupled to a cavity that is valid in all regimes of light-matter coupling. We compare two different approaches to obtain thermal Green functions. We provide a detailed application of the theory to the Quantum Hall effect and to a collection of magnetic models.
  arXiv  Detail & Related papers  (2024-06-17T18:00:07Z)
• Inverse problem in energy-dependent potentials using semiclassical methods [0.0]
  We use the semi-classical WKB method to first revisit the perturbation of bound states of potential wells and reflection/transmission coefficients. We then discuss the inverse problem, in which the latter observables are used to reconstruct the properties of the potentials.
  arXiv  Detail & Related papers  (2024-04-17T15:33:34Z)
• $\widetilde{O}(N^2)$ Representation of General Continuous Anti-symmetric Function [41.1983944775617]
  In quantum mechanics, the wave function of fermion systems such as many-body electron systems are anti-symmetric and continuous. We prove that our ansatz can represent any AS continuous functions, and can accommodate the determinant-based structure proposed by Hutter.
  arXiv  Detail & Related papers  (2024-02-23T07:59:41Z)
• Exactly Solvable Schr\"odinger equations with Singularities: A Systematic Approach to Solving Complexified Potentials (part1) [0.0]
  Extending the argument of the potential to a complex number leads to solving exactly the Schr"odinger equation. This paper gives a new perspective on how to solve the second-order linear differential equation written in normal form.
  arXiv  Detail & Related papers  (2023-01-10T05:39:43Z)
• An application of the HeunB function [0.0]
  How does the inclusion of the gravitational potential alter an otherwise exact quantum mechanical result? The Schrodinger equation for the reduced mass is then solved to obtain the parabolic cylinder functions as eigenfunctions and the eigenvalues of the reduced Hamiltonian are calculated exactly. The eigenvalues are the determined from a recent series expansion in terms of the Hermite functions for the solution of the differential equation whose exact solution is the aforesaid HeunB function.
  arXiv  Detail & Related papers  (2022-12-17T17:04:49Z)
• Energy spectrum design and potential function engineering [0.0]
  We give a local numerical realization of the potential function associated with the chosen energy spectrum. The potential function is obtained only for a given set of physical parameters.
  arXiv  Detail & Related papers  (2022-11-17T04:33:01Z)
• Equivariant Energy-Guided SDE for Inverse Molecular Design [35.50806745435793]
  EEGSDE is a flexible framework for controllable 3D molecule generation under the guidance of an energy function. EEGSDE is able to generate molecules with multiple target properties by combining the corresponding energy functions linearly.
  arXiv  Detail & Related papers  (2022-09-30T12:10:15Z)
• Learning Energy Networks with Generalized Fenchel-Young Losses [34.46284877812228]
  Energy-based models, a.k.a. energy networks, perform inference by optimizing an energy function. We propose generalized Fenchel-Young losses, a natural loss construction for learning energy networks.
  arXiv  Detail & Related papers  (2022-05-19T14:32:04Z)
• Deformed Explicitly Correlated Gaussians [58.720142291102135]
  Deformed correlated Gaussian basis functions are introduced and their matrix elements are calculated. These basis functions can be used to solve problems with nonspherical potentials.
  arXiv  Detail & Related papers  (2021-08-10T18:23:06Z)
• Variational Monte Carlo calculations of $\mathbf{A\leq 4}$ nuclei with an artificial neural-network correlator ansatz [62.997667081978825]
  We introduce a neural-network quantum state ansatz to model the ground-state wave function of light nuclei. We compute the binding energies and point-nucleon densities of $Aleq 4$ nuclei as emerging from a leading-order pionless effective field theory Hamiltonian.
  arXiv  Detail & Related papers  (2020-07-28T14:52:28Z)
• Construction of potential functions associated with a given energy spectrum [0.0]
  We present a method that gives the class of potential functions for exactly solvable problems corresponding to a given energy spectrum. In this work, we study the class of problems with a mix of continuous and discrete energy spectrum that are associated with the continuous dual Hahn.
  arXiv  Detail & Related papers  (2020-02-05T14:30:26Z)

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.