English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

p-Adic quantum mechanics is constructed from the Dirac-von Neumann axiomsidentifying quantum states with square-integrable functions on theN-dimensional p-adic space, Q_{p}^{N}. This choice is equivalent to thehypothesis of the discreteness of the space. The time is assumed to be a realvariable. p-Adic quantum mechanics is the response to the question: whathappens with the standard quantum mechanics if the space has a discrete nature?The time evolution of a quantum state is controlled by a nonlocal Schr\"odingerequation obtained from a p-adic heat equation by a temporal Wick rotation. Thisp-adic heat equation describes a particle performing a random motion inQ_{p}^{N}. The Hamiltonian is a nonlocal operator; thus, the Schr\"odingerequation describes the evolution of a quantum state under nonlocalinteractions. In this framework, the Schr\"odinger equation admitscomplex-valued plane wave solutions, which we interpret as p-adic de Brogliewaves. These mathematical waves have all wavelength p^{-1}. Then, in the p-adicframework, the double-slit experiment cannot be explained using theinterference of the de Broglie waves. The wavefunctions can be represented asconvergent series in the de Broglie waves. Then, these functions are justmathematical objects. Only the square of the modulus of a wave function has aphysical meaning as a time-dependent probability density. These probabilitydensities exhibit the classical interference patterns produced by `quantumwaves.' In the p-adic framework, in the double-slit experiment, each particlegoes through one slit only. Finally, we propose that the classical de Brogliewave-particle duality is a manifestation of the discreteness of space-time.

The p-Adic Schr\"odinger Equation and the Two-slit Experiment in Quantum Mechanics