arXiv subjects

Agung Budiyono

Publications and source records attributed to Agung Budiyono.

40 records · Page 3Linked to original sources

arXiv2009

Spatiotemporally-localized-stationary typical wave function satisfying Klein-Gordon equation with emergent mass

Starting from relativistic mass-less Madelung fluid, we shall develop a class of typical wave functions by imposing it to maximize Shannon entropy given its finite average quantum potential. We show that there is a class of solutions in which the wave function is spatiotemporally localized with finite spacetime support, uniformly moving hence stationary. It turns out that the quantum amplitude satisfies Klein-Gordon equation with emergent mass term proportional to the square root of average quantum potential. We show that there is physical time uncertainty which decreases as the mass increases. We also rederive the classical energy-momentum relation provided the de Broglie-Einstein relation holds. In this case, the time uncertainty is proportional to the inverse of classical energy.

quant-ph↗

arXiv2009

The most probable wave function of a single free moving particle

We develop the most probable wave functions for a single free quantum particle given its momentum and energy by imposing its quantum probability density to maximize Shannon information entropy. We show that there is a class of solutions in which the quantum probability density is self-trapped with finite-size spatial support, uniformly moving hence keeping its form unchanged.

quant-ph↗

arXiv2009

A Class of Self-Trapped and Self-Focusing Wave Functions in Madelung Fluid Picture of A Single Free Particle Quantum System

Using the Madelung fluid picture of Schrödinger equation for a single free particle moving in one spatial dimension, we shall specify a class of wave functions whose quantum probability density is being trapped by the quantum potential it itself generates. The global convexity of the quantum potential generated by the initial self-trapped wave function will then be shown to further localize the quantum probability density through a self-generated focusing equation for a finite interval of time.

quant-ph↗

arXiv2009

Madelung Fluid Model for The Most Likely Wave Function of a Single Free Particle in Two Dimensional Space with a Given Average Energy

We consider spatially two dimensional Madelung fluid whose irrotational motion reduces into the Schrödinger equation for a single free particle. In this respect, we regard the former as a direct generalization of the latter, allowing a rotational quantum flow. We then ask for the most likely wave function possessing a given average energy by maximizing the Shannon information entropy over the quantum probability density. We show that there exists a class of solutions in which the wave function is self-trapped, rotationally symmetric, spatially localized with finite support, and spinning around its center, yet stationary. The stationarity comes from the balance between the attractive quantum force field of a trapping quantum potential generated by quantum probability density and the repulsive centrifugal force of a rotating velocity vector field. We further show that there is a limiting case where the wave function is non-spinning and yet still stationary. This special state turns out to be the lowest stationary state of the ordinary Schrödinger equation for a particle in a cylindrical tube classical potential.

quant-ph↗