Hamiltonian Formulation of the Pilot-Wave Theory

• URL: http://arxiv.org/abs/2101.10117v1
• Date: Thu, 21 Jan 2021 23:52:38 GMT
• Title: Hamiltonian Formulation of the Pilot-Wave Theory
• Authors: Dan N. Vollick
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In the pilot-wave theory of quantum mechanics particles have definite positions and velocities and the system evolves deterministically. The velocity of a particle is determined by the wave function of the system (the guidance equation) and the wave function evolves according to Schrodinger's equation. In this paper 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.

Related papers

• Derivation of Schrodinger's equation from the Hamilton-Jacobi and the Eikonal equations [0.0]
  We give a detailed derivation of Schrodinger's equation from the Hamilton-Jacobi equation and the Eikonal equation in geometrical optics. We derive Born's statistical rule using the early understanding of de Broglie that both particles and waves exist.
  arXiv  Detail & Related papers  (2024-09-21T12:54:26Z)
• 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)
• Exact quantum-mechanical equations for particle beams [91.3755431537592]
  These equations present the exact generalizations of the well-known paraxial equations in optics. Some basic properties of exact wave eigenfunctions of particle beams have been determined.
  arXiv  Detail & Related papers  (2022-06-29T20:39:36Z)
• Wave-particle duality and the zitterbewegung [0.0]
  We show that a free spinless quantum particle moving with velocity v obeys the standard wave equation of electro-magnetism. We also discuss the implications for the zitterbewegung problem and its relationship to isotropy.
  arXiv  Detail & Related papers  (2021-07-19T17:17:26Z)
• Classical and Quantum Brownian Motion [0.0]
  In quantum mechanics electrons and other point particles are no waves and the chapter of quantum mechanics originated for the force carriers. A new projector operator is proposed for the collapse of the wave function of a quantum particle moving in a classical environment. Considering the Brownian dynamics in the frames of the Bohmian mechanics, the density functional Bohm-Langevin equation is proposed.
  arXiv  Detail & Related papers  (2021-05-12T13:24:39Z)
• 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)
• The Time-Evolution of States in Quantum Mechanics [77.34726150561087]
  It is argued that the Schr"odinger equation does not yield a correct description of the quantum-mechanical time evolution of states of isolated (open) systems featuring events. A precise general law for the time evolution of states replacing the Schr"odinger equation is formulated within the so-called ETH-Approach to Quantum Mechanics.
  arXiv  Detail & Related papers  (2021-01-04T16:09:10Z)
• 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.