Path integral solution to a charged particle in an infinite square-well potential with a constant electric field

1994 ◽  
Vol 72 (9-10) ◽  
pp. 591-595 ◽  
Author(s):  
Kyu Hwang Yeon ◽  
Chung-In Um ◽  
Thomas F. George ◽  
Lakshmi N. Pandey
Keyword(s):  
Wave Function ◽  
Charged Particle ◽  
Electric Field ◽  
Path Integration ◽  
Uncertainty Relation ◽  
Constant Electric Field ◽  
Integral Solution ◽  
One Dimension ◽  
Feynman Path ◽  
Square Well

The propagator of a charged particle in an infinite square-well potential in one dimension with a constant electric field is solved exactly using Feynman path integration. The wave function of the system is evaluated by the propagator. This wave function depends on time in a way determined by the well size, particle mass and charge, and applied electric field. The uncertainty relation of the system is also obtained by this function.

scholarly journals Trapping and transport of charges in DNA by mobile discrete breathers

2018 ◽  
Vol 13 (1) ◽  
pp. 1-12 ◽  
Author(s):  
A.P. Chetverikov ◽  
K.S. Sergeev ◽  
V.D. Lakhno
Keyword(s):  
Numerical Simulation ◽  
Wave Function ◽  
Charged Particle ◽  
Electric Field ◽  
External Electric Field ◽  
Base Pair ◽  
Quasi Particle ◽  
Dna Molecule ◽  
Discrete Breathers

Numerical simulation of trapping and transport of a charged particle (electron or hole) by mobile discrete breathes (mobile DB, MDB) in DNA molecule has been provided. Mobile DBs have been excited by disturbance of displacements or velocities of adjacent nucleotide pairs dislocated near one of fixed ends of the molecule. It is shown that effective forming of a stable quasi-particle “MDB + electron” occurs when a few of nucleotide pairs at the end of DNA are excited. Breathes may be excited by disturbances of displacements and velocities directed both to axis and from axis of the molecule. A wave function of an electron must be located initially in a region of disturbance of the molecule. It has been found that a metastable quasi-particle may be transported at a distance up to 200 of a rise per base pair. The mechanism of transport of a charged particle presented is not in need of an external electric field and may be considered as an alternative one to the polaronic mechanism.

The Schrödinger Equation, Path Integration and Applications

2021 ◽  
Vol 15 (01) ◽  
pp. 61-75
Author(s):  
Everaldo M. Bonotto ◽  
Felipe Federson ◽  
Márcia Federson
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Path Integration ◽  
Schrodinger Equation ◽  
Feynman Integral ◽  
Feynman Path Integral ◽  
Feynman Path ◽  
Henstock Integral ◽  
The Mean

The Schrödinger equation is fundamental in quantum mechanics as it makes it possible to determine the wave function from energies and to use this function in the mean calculation of variables, for example, as the most likely position of a group of one or more massive particles. In this paper, we present a survey on some theories involving the Schrödinger equation and the Feynman path integral. We also consider a Feynman–Kac-type formula, as introduced by Patrick Muldowney, with the Henstock integral in the description of the expectation of random walks of a particle. It is well known that the non-absolute integral defined by R. Henstock “fixes” the defects of the Feynman integral. Possible applications where the potential in the Schrödinger equation can be highly oscillating, discontinuous or delayed are mentioned in the end of the paper.

A SIMPLE HAMILTONIAN MODEL OF RUNAWAY PARTICLE WITH SINGULAR INTERACTION

2005 ◽  
Vol 15 (05) ◽  
pp. 753-766 ◽  
Author(s):  
PAOLO BUTTÀ ◽  
FRANCESCO MANZO ◽  
CARLO MARCHIORO
Keyword(s):  
Charged Particle ◽  
Hamiltonian System ◽  
Electric Field ◽  
Particle Velocity ◽  
Electric Field Intensity ◽  
Constant Electric Field ◽  
One Dimensional ◽  
Accelerated Motion ◽  
Hamiltonian Model ◽  
Particle Medium

We consider a Hamiltonian system given by a charged particle under the action of a constant electric field and interacting with a medium, which is described as a Vlasov fluid. We assume that the action of the charged particle on the fluid is negligible and that the latter has one-dimensional symmetry. We prove that if the singularity of the particle/medium interaction is integrable and the electric field intensity is large enough, then the particle escapes to infinity with a quasi-uniformly accelerated motion. A key tool in the proof is a new estimate on the growth in time of the fluid particle velocity for one-dimensional Vlasov fluids with bounded interactions.

scholarly journals Phonon residual resistance of pure crystals

2015 ◽  
Vol 29 (29) ◽  
pp. 1550206
Author(s):  
A. I. Agafonov
Keyword(s):  
Electric Field ◽  
Constant Electric Field ◽  
Finite Thickness ◽  
Mean Free Path ◽  
Residual Resistivity ◽  
Boltzmann Transport ◽  
Residual Resistance ◽  
Temperature Resistance ◽  
Electron Mean Free Path ◽  
The Ideal

In this paper, using the Boltzmann transport equation, we study the zero temperature resistance of perfect metallic crystals of a finite thickness d along which a weak constant electric field E is applied. This resistance, hereinafter referred to as the phonon residual resistance, is caused by the inelastic scattering of electrons heated by the electric field, with emission of long-wave acoustic phonons and is proportional to [Formula: see text]. Consideration is carried out for Cu, Ag and Au perfect crystals with the thickness of about 1 cm, in the fields of the order of 1 mV/cm. Following the Matthiessen rule, the resistance of the pure crystals, the thicknesses of which are much larger than the electron mean free path is represented as the sum of both the impurity and phonon residual resistances. The condition on the thickness and field is found at which the low-temperature resistance of pure crystals does not depend on their purity and is determined by the phonon residual resistivity of the ideal crystals. The calculations are performed for Cu with a purity of at least 99.9999%.

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