Energy spectrum design and potential function engineering

• URL: http://arxiv.org/abs/2211.09329v1
• Date: Thu, 17 Nov 2022 04:33:01 GMT
• Title: Energy spectrum design and potential function engineering
• Authors: A. D. Alhaidari and T. J. Taiwo
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Starting with an orthogonal polynomial sequence $\{p_n(s)\}_{n=0}^\infty$ that has a discrete spectrum, we design an energy spectrum formula, $E_k = f (s_k)$, where $|{s_k\}$ is the finite or infinite discrete spectrum of the polynomial. Using a recent approach for doing quantum mechanics based, not on potential functions but, on orthogonal energy polynomials, we give a local numerical realization of the potential function associated with the chosen energy spectrum. In this work, we select the three-parameter continuous dual Hahn polynomial as an example. Exact analytic expressions are given for the corresponding bound states energy spectrum, scattering states phase shift, and wavefunctions. However, the potential function is obtained only numerically for a given set of physical parameters.

Related papers

• Equivariant Graph Network Approximations of High-Degree Polynomials for Force Field Prediction [62.05532524197309]
  equivariant deep models have shown promise in accurately predicting atomic potentials and force fields in molecular dynamics simulations. In this work, we analyze the equivariant functions for equivariant architecture, and introduce a novel equivariant network, named PACE. As experimented in commonly used benchmarks, PACE demonstrates state-of-the-art performance in predicting atomic energy and force fields.
  arXiv  Detail & Related papers  (2024-11-06T19:34:40Z)
• Neural Pfaffians: Solving Many Many-Electron Schrödinger Equations [58.130170155147205]
  Neural wave functions accomplished unprecedented accuracies in approximating the ground state of many-electron systems, though at a high computational cost. Recent works proposed amortizing the cost by learning generalized wave functions across different structures and compounds instead of solving each problem independently. This work tackles the problem by defining overparametrized, fully learnable neural wave functions suitable for generalization across molecules.
  arXiv  Detail & Related papers  (2024-05-23T16:30:51Z)
• Spectral solutions for the Schr\"odinger equation with a regular singularity [0.0]
  We attempt the exact quantization conditions (EQC) for the quantum periods associated with potentials V (x) which are singular at the origin. We validate our EQC proposition by numerically computing the Voros spectrum and matching it with the true spectrum for |x| potential. We have given a route to obtain the spectral solution for the one dimensional Schr"odinger equation involving potentials with regular singularity at the origin.
  arXiv  Detail & Related papers  (2023-08-31T13:05:59Z)
• $O(N^2)$ Universal Antisymmetry in Fermionic Neural Networks [107.86545461433616]
  We propose permutation-equivariant architectures, on which a determinant Slater is applied to induce antisymmetry. FermiNet is proved to have universal approximation capability with a single determinant, namely, it suffices to represent any antisymmetric function. We substitute the Slater with a pairwise antisymmetry construction, which is easy to implement and can reduce the computational cost to $O(N2)$.
  arXiv  Detail & Related papers  (2022-05-26T07:44:54Z)
• A Note on Shape Invariant Potentials for Discretized Hamiltonians [0.0]
  We show that the energy spectra and wavefunctions for discretized Quantum Mechanical systems can be found using the technique of N=2 Supersymmetric Quantum Mechanics.
  arXiv  Detail & Related papers  (2022-05-20T11:34:07Z)
• On the exactly-solvable semi-infinite quantum well of the non-rectangular step-harmonic profile [0.0]
  The model behaves itself as a semi-infinite quantum well of the non-rectangular profile. We show that wavefunctions of the discrete spectrum recover wavefunctions in terms of the Hermites. We also present a new limit relation that reduces Bessels directly to Hermites.
  arXiv  Detail & Related papers  (2021-11-07T12:23:17Z)
• Quantum Simulation of Molecules without Fermionic Encoding of the Wave Function [62.997667081978825]
  fermionic encoding of the wave function can be bypassed, leading to more efficient quantum computations. An application to computing the ground-state energy and 2-RDM of H$_4$ is presented.
  arXiv  Detail & Related papers  (2021-01-27T18:57:11Z)
• $\mathcal{P}$,$\mathcal{T}$-odd effects for RaOH molecule in the excited vibrational state [77.34726150561087]
  Triatomic molecule RaOH combines the advantages of laser-coolability and the spectrum with close opposite-parity doublets. We obtain the rovibrational wave functions of RaOH in the ground electronic state and excited vibrational state using the close-coupled equations derived from the adiabatic Hamiltonian.
  arXiv  Detail & Related papers  (2020-12-15T17:08:33Z)
• 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)
• 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)
• 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.