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- Title
Stationary Schrödinger Equation and Darwin Term from Maximal Entropy Random Walk.
- Authors
Faber, Manfried
- Abstract
We describe particles in a potential by a special diffusion process, the maximal entropy random walk (MERW) on a lattice. Since MERW originates in a variational problem, it shares the linear algebra of Hilbert spaces with quantum mechanics. The Born rule appears from measurements between equilibrium states in the past and the same equilibrium states in the future. Introducing potentials by the observation that time, in a gravitational field running in different heights with a different speed, MERW respects the rule that all trajectories of the same duration are counted with equal probability. In this way, MERW allows us to derive the Schrödinger equation for a particle in a potential and the Darwin term of the nonrelativistic expansion of the Dirac equation. Finally, we discuss why quantum mechanics cannot be simply a result of MERW, but, due to the many analogies, MERW may pave the way for further understanding.
- Subjects
SCHRODINGER equation; RANDOM walks; QUANTUM mechanics; HILBERT algebras; ENTROPY; NONRELATIVISTIC quantum mechanics; HILBERT space; DIRAC equation
- Publication
Particles (2571-712X), 2024, Vol 7, Issue 1, p25
- ISSN
2571-712X
- Publication type
Article
- DOI
10.3390/particles7010002