Bohmian trajectories and the Path Integral Paradigm. Complexified Lagrangian Mechanics
arXiv:0808.1245 · doi:10.1142/S0218127409024104
Abstract
David Bohm shown that the Schr{ö}dinger equation, that is a "visiting card" of quantum mechanics, can be decomposed onto two equations for real functions - action and probability density. The first equation is the Hamilton-Jacobi (HJ) equation, a "visiting card" of classical mechanics, to be modified by the Bohmian quantum potential. And the second is the continuity equation. The latter can be transformed to the entropy balance equation. The Bohmian quantum potential is transformed to two Bohmian quantum correctors. The first corrector modifies kinetic energy term of the HJ equation, and the second one modifies potential energy term. Unification of the quantum HJ equation and the entropy balance equation gives complexified HJ equation containing complex kinetic and potential terms. Imaginary parts of these terms have order of smallness about the Planck constant. The Bohmian quantum corrector is indispensable term modifying the Feynman's path integral by expanding coordinates and momenta to imaginary sector.
14 pages, 3 figures, 46 references, 48 equations
References in corpus (14)
- Decoherence of matter waves by thermal emission of radiation
- A trajectory-based understanding of quantum interference
- Decoherence in a Talbot Lau interferometer: the influence of molecular scattering
- Quantum mechanics: Myths and facts
- A causal look into the quantum Talbot effect
- Wave and Particle in Molecular Interference Lithography
- De Broglie-Bohm Guidance Equations for Arbitrary Hamiltonians
- Flux Continuity and Probability Conservation in Complexified Bohmian Mechanics
- Reconciling Semiclassical and Bohmian Mechanics: II. Scattering states for discontinuous potentials
- Monte Carlo Generation of Bohmian Trajectories
- Matter waves in the Talbot-Lau interferometry
- N-Slit Interference: Fractals in Near-Field Region, Bohmian Trajectories
- Specification of the Q Hypothesis: An Alternative Mathematical Foundation for Physics
- Quantum Mechanics with Trajectories: Quantum Trajectories and Adaptive Grids
Cited by in corpus (9)
- Physical vacuum is a special superfluid medium
- Hydrodynamics of the Physical Vacuum: I. Scalar quantum sector
- Hydrodynamics of Superfluid Quantum Space: de Broglie interpretation of the quantum mechanics
- Quantum consciousness in warm, wet, and noisy brain
- From the Newton's laws to motions of the fluid and superfluid vacuum: vortex tubes, rings, and others
- Droplets moving on a fluid surface: interference pattern from two slits
- A Thermodynamical derivation of the quantum potential and the temperature of the wave function
- A Study on the Scattering of Matter Waves through Slits
- Ensemble in phase space: statistical formalism of quantum mechanics