Schrodinger's Field Equation

• URL: http://arxiv.org/abs/2505.05496v1
• Date: Mon, 05 May 2025 23:03:33 GMT
• Title: Schrodinger's Field Equation
• Authors: Jacek Mroczkowski,
• Abstract summary: The potential energies of electron states in the hydrogen atom were determined using the operator formalism in the Schrodinger nonrelativistic equation.<n>All total kinetic and potential energies conformed with the well known 1/n2 rule.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The intrinsic and dynamic kinetic energies, and the potential energies of electron states in the hydrogen atom, were determined using the operator formalism in the Schrodinger nonrelativistic equation. Intrinsic energies were determined using the momentum operator, while the additional dynamic energies of the spinning fields were determined using the angular momentum operator. All 10 states up to the principal quantum number n = 3 and all m states of n = 7, l = 3 were analyzed. The two forms of kinetic energy can only be explained with an electron field representation. All total kinetic and potential energies conformed with the well known 1/n^2 rule. Angular momentum analysis of the 2P1/2 states provided a field spinning rate; in addition, the dynamic kinetic energy of the spinning field determined by both operator analysis and explicit calculation based on the spinning rate gave the same energy results.

Related papers

• A non-hermitean momentum operator for the particle in a box [49.1574468325115]
  We show how to construct the corresponding hermitean Hamiltonian for the infinite as well as concrete example. The resulting Hilbert space can be decomposed into a physical and unphysical subspace.
  arXiv  Detail & Related papers  (2024-03-20T12:51:58Z)
• Is the effective potential, effective for dynamics? [8.273855626116564]
  Energy conservation leads to the emergence of highly excited, entangled stationary states from the dynamical evolution. The results suggest novel characterization of equilibrium states in terms of order parameter vs. energy density.
  arXiv  Detail & Related papers  (2024-03-11T18:19:06Z)
• Coherent energy and force uncertainty in deep learning force fields [10.2454262799094]
  We propose a machine learning potential energy model in which energy and force aleatoric uncertainty are linked through a spatially correlated noise process. We demonstrate our approach on an equivariant messages passing neural network potential trained on energies and forces on two out-of-equilibrium molecular datasets.
  arXiv  Detail & Related papers  (2023-12-07T09:49:05Z)
• 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)
• Derivation of the Schr\"odinger equation from QED [0.0]
  The Schr"odinger equation relates the electron wavefunction and the electric potential. We show that, in low energy interactions, the electric potential accurately represents the contributions of the intermediate photon exchanges.
  arXiv  Detail & Related papers  (2022-12-23T13:48:56Z)
• Partition of kinetic energy and magnetic moment in dissipative diamagnetism [20.218184785285132]
  We analyze dissipative diamagnetism, arising due to dissipative cyclotron motion in two dimensions, in the light of the quantum counterpart of energy equipartition theorem. The expressions for kinetic energy and magnetic moment are reformulated in the context of superstatistics.
  arXiv  Detail & Related papers  (2022-07-30T08:07:28Z)
• Fields and Equations of Classical Mechanics for Quantum Mechanics [0.0]
  An equation is also derived that is equivalent to the main equation of Bohmian mechanics. For one-body systems, the Eulerian Eq. can model either a fluid or particle description of quantum states.
  arXiv  Detail & Related papers  (2022-07-09T23:28:27Z)
• Correspondence Between the Energy Equipartition Theorem in Classical Mechanics and its Phase-Space Formulation in Quantum Mechanics [62.997667081978825]
  In quantum mechanics, the energy per degree of freedom is not equally distributed. We show that in the high-temperature regime, the classical result is recovered.
  arXiv  Detail & Related papers  (2022-05-24T20:51:03Z)
• Restrictions imposed by the wave function on the results of measurements of the particle momentum [0.0]
  It is shown that knowing the wave function implies not only statistical restrictions on the measurement results. A key role in establishing the physical meaning of these fields is played by the fact that the field of the kinetic energy operator contains two heterogeneous contributions.
  arXiv  Detail & Related papers  (2021-11-09T16:21:40Z)
• The generalized Hamilton principle and non-Hermitian quantum theory [7.151354616862258]
  The Hamilton principle is a variation principle describing the isolated and conservative systems. By Feynman path integration, we can obtain the Hermitian quantum theory, i.e., the standard Schrodinger equation.
  arXiv  Detail & Related papers  (2021-10-09T09:29:06Z)
• Quantum dynamics of a one degree-of-freedom Hamiltonian saddle-node bifurcation [0.0]
  We study the quantum dynamics of a one degree-of-freedom (DOF) Hamiltonian that is a normal form for a saddle node bifurcation of equilibrium points in phase space. The main focus is to evaluate the effect of the depth of the well on the quantum dynamics.
  arXiv  Detail & Related papers  (2021-07-02T11:30:17Z)
• On the Extension of Linear Damping to Quantum Mechanics through Fractionary Momentum Operators Pt. I [2.5582075465437972]
  Three important associated 1 dimensional problems were solved: the free particle case, the infinite potential well, and the harmonic potential. We conclude that there exists a relationship between fractional kinetic energy and special relativity energies, that remains unclear and needs further exploration.
  arXiv  Detail & Related papers  (2020-07-15T02:12:06Z)

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.