Derivation of the Schrodinger equation from fundamental principles

• URL: http://arxiv.org/abs/2603.27041v1
• Date: Fri, 27 Mar 2026 23:12:55 GMT
• Title: Derivation of the Schrodinger equation from fundamental principles
• Abstract summary: We derive the Schrodinger equation for the particle wave function, assuming that it has a meaning of the probability amplitude to find the particle at time t at point r.
• Score: 0.17188280334580197
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Schrodinger path to the quantum mechanical wave equation was heuristic and guided more by physical intuition than formal deduction. Here we derive the Schrodinger equation for the particle wave function, assuming that it has a meaning of the probability amplitude to find the particle at time t at point r and the relations E=hw, p=hk expressing particle energy and momentum in terms of the frequency and wave vector of the associated probability wave.

Related papers

• 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)
• Dirac, Schroedinger, and Maxwell equations in scalar and vector field quantum mechanics [0.0]
  The quantum theory of relativistic particles is reconsidered on the basis of a photon-like dispersion relation.<n>The wave-particle duality can be redefined as the electromagnetic wave-particle duality.
  arXiv  Detail & Related papers  (2025-08-20T10:04:21Z)
• 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)
• Analogue black string in a quantum harmonic oscillator [49.1574468325115]
  We write the exact solution of the Klein-Gordon equation in the background of a chargeless, static black string.<n>The eigenvalue problem provides complex energy values for the particle, which may indicate the presence of quasinormal modes.<n>We show a simple quantum system that can imitate the particle in the black string background, whose solutions are also applications of the biconfluent Heun function.
  arXiv  Detail & Related papers  (2024-12-31T15:03:57Z)
• A Theory of Quantum Jumps [44.99833362998488]
  We study fluorescence and the phenomenon of quantum jumps'' in idealized models of atoms coupled to the quantized electromagnetic field. Our results amount to a derivation of the fundamental randomness in the quantum-mechanical description of microscopic systems.
  arXiv  Detail & Related papers  (2024-04-16T11:00:46Z)
• The p-Adic Schrödinger Equation and the Two-slit Experiment in Quantum Mechanics [0.0]
  p-Adic quantum mechanics is constructed from the Dirac-von Neumann axioms. The p-adic quantum mechanics is motivated by the question: what happens with the standard quantum mechanics if the space has a discrete nature?
  arXiv  Detail & Related papers  (2023-08-02T17:10:10Z)
• 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)
• Free expansion of a Gaussian wavepacket using operator manipulations [77.34726150561087]
  The free expansion of a Gaussian wavepacket is a problem commonly discussed in undergraduate quantum classes. We provide an alternative way to calculate the free expansion by recognizing that the Gaussian wavepacket can be thought of as the ground state of a harmonic oscillator. As quantum instruction evolves to include more quantum information science applications, reworking this well known problem using a squeezing formalism will help students develop intuition for how squeezed states are used in quantum sensing.
  arXiv  Detail & Related papers  (2023-04-28T19:20:52Z)
• 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)
• Traveling Wave Form Description for Dirac Field and Its Deduction To Pauli Equation Type Forms in Quantum Mechanics [7.6915316507201785]
  We derive an equivalent traveling wave form description for Dirac field. In the non-relativistic limit, such form can reduce to inverse-Galilean transformed Schrodinger-type equation.
  arXiv  Detail & Related papers  (2022-03-17T00:48:50Z)
• Fall of Quantum Particle to the Center: Exact results [0.0]
  The fall of a particle to the center of a singular potential U(r) is one of a few fundamental problems of quantum mechanics. It is shown that the known necessary conditions for the particle to fall simultaneously are sufficient.
  arXiv  Detail & Related papers  (2021-08-04T11:44:20Z)
• Schrodinger's Equation is Universal, Dark Matter and Double Diffusion [0.0]
  This paper considers a main particle and an incident particle classical mechanics elastic collision preserving energy and momentum. The main result of the paper shows that the colliding two particle classical Hamiltonian energy can be represented in four weighted individual particle. The Schrodinger equation can also be used to represent corrections for Newton's equation and suggests a user profile to be used in the search for Dark Matter.
  arXiv  Detail & Related papers  (2021-05-05T11:02:37Z)
• Hamiltonian Formulation of the Pilot-Wave Theory [0.0]
  In pilot-wave theory of quantum mechanics particles have definite positions and velocities and the system evolves deterministically. I first construct a Hamiltonian that gives Schrodinger's equation and the guidance equation for the particle. I then find the Hamiltonian for a relativistic particle in Dirac's theory and for a quantum scalar field.
  arXiv  Detail & Related papers  (2021-01-21T23:52:38Z)
• 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.