Principle and approach of boundary extraction based on particle motion in quantum mechanics

2007 ◽  
Vol 46 (2) ◽  
pp. 027005 ◽  
Author(s):  
Mingyue Ding
Keyword(s):  
Quantum Mechanics ◽  
Particle Motion ◽  
Boundary Extraction

scholarly journals On similarity solutions, curved particle motion and artificial gravitation: A case for hydrogen

2021 ◽  
Vol 20 ◽  
pp. 40-47
Author(s):  
JM Manale
Keyword(s):  
Quantum Mechanics ◽  
Hydrogen Atom ◽  
Particle Motion ◽  
Gravitational Constant ◽  
Initial Conditions ◽  
Similarity Solutions ◽  
Newtonian Mechanics ◽  
External Forces

We demonstrate that suitable initial conditions exist for a particle motion along a curved path, like a circle, without any external forces acting on it. This we achieve by diverting from the popular practice of describing motions of macroscopic bodies through Newtonian mechanics, and instead opt for quantum mechanics. This we do for the hydrogen atom. The validity of the idea is demonstrated by presenting a formula for G, the universal gravitational constant.

Conditions for a Solitonic Solution of the Doener–Goldin Equation of Quantum Mechanics

1998 ◽  
Vol 12 (13) ◽  
pp. 519-527
Author(s):  
E. C. Caparelli ◽  
S. S. Mizrahi ◽  
V. V. Dodonov
Keyword(s):  
Quantum Mechanics ◽  
Nonlinear Equation ◽  
Plane Wave ◽  
Gauge Transformation ◽  
Particle Motion ◽  
Continuity Equation ◽  
Free Particle ◽  
Solitonic Solution ◽  
The Mean ◽  
Nonlinear Gauge

A solitonic solution to the free-particle motion of Doebner–Goldin nonlinear equation is shown to exist under special conditions. For small values of the nonlinearity parameters, the solution is a plane wave modulated by a cos function, and the solitonic one arises when the parameters surpass some critical values. The mean energy of the particle is a conserved quantity and the continuity equation holds. We also verify that there is no nonlinear gauge transformation (in the sense of Ref. 12) that linearizes that equation.

scholarly journals On Symmetry, Lie Symmetry and Curved Path Particle Motion: a Case for Hydrogen

2021 ◽  
Vol 15 ◽  
pp. 24-26
Author(s):  
JM Manale
Keyword(s):  
Quantum Mechanics ◽  
Hydrogen Atom ◽  
External Force ◽  
Particle Motion ◽  
Gravitational Constant ◽  
Lie Symmetry ◽  
Newtonian Mechanics

We divert from popular practice by describing a motion of a macroscopic body, a hydrogen atom in this case, through quantum mechanics. What we realise is that a body can follow a curved path, without any external force acting on it, which is in contrast to Newtonian mechanics. To test the idea, we determine a formula for G, the universal gravitational constant.

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