Classical and quantum particles in the brachistochrone upper half-space

被引：0

作者：

Mazharimousavi, S. Habib ^{[1
]}

机构：

[1] Eastern Mediterranean Univ, Fac Arts & Sci, Dept Phys, North Cyprus Via Mersin 10, Famagusta, North Cyprus, Turkey

来源：

EUROPEAN PHYSICAL JOURNAL PLUS | 2022年 / 137卷 / 11期

关键词：

BOUNDED SPIN-1/2 PARTICLES; DEPENDENT EFFECTIVE MASSES; CURVED SPACES; MECHANICS; OSCILLATOR; MODEL; SUPERSYMMETRY; UNCERTAINTY; SCHRODINGER; SYSTEMS;

D O I：

10.1140/epjp/s13360-022-03466-0

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The brachistochrone upper half-space geometry is introduced and investigated. The classical geodesics on this curved space are found to be planar cycloids. We show that the center and radius of the cycloid depend on the initial conditions. Furthermore, we solve the Schrodinger equation for a free particle in this curved space. Due to the geometrical structure of the curved space, the free particle-free means no external nongeometric potential is applied-experiences a purely geometric potential. We utilize the point canonical transformation to bring the Schrodinger equation into its standard form where the geometric potential takes the form of a harmonic oscillator.

引用

页数：8

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