The One-dimensional Fractional Supersymmetric Quantum Mechanical Operator of Momentum

2007 ◽  
Vol 16 (1-2) ◽  
pp. 213-221 ◽  
Author(s):  
Paulius Miškinis
Keyword(s):  
Quantum Mechanical ◽  
One Dimensional ◽  
The One ◽  
Quantum Mechanical Operator ◽  
Mechanical Operator

scholarly journals On the Spectrum of the Local $${\mathbb {P}}^2$$ Mirror Curve

2020 ◽  
Vol 21 (11) ◽  
pp. 3479-3497
Author(s):  
Rinat Kashaev ◽  
Sergey Sergeev
Keyword(s):  
Spectral Problem ◽  
Bethe Ansatz ◽  
Quantum Mechanical ◽  
Planck’S Constant ◽  
Transcendental Equations ◽  
Del Pezzo ◽  
Planck's Constant ◽  
Quantum Mechanical Operator ◽  
Mechanical Operator

Abstract We address the spectral problem of the formally normal quantum mechanical operator associated with the quantised mirror curve of the toric (almost) del Pezzo Calabi–Yau threefold called local $${\mathbb {P}}^2$$ P 2 in the case of complex values of Planck’s constant. We show that the problem can be approached in terms of the Bethe ansatz-type highly transcendental equations.

scholarly journals Schrodinger Wave Equation

2020 ◽  
Vol 4 (1) ◽  
Author(s):  
Aaron C.H. Davey
Keyword(s):  
Quantum Mechanics ◽  
Wave Equation ◽  
Quantum Theory ◽  
System Change ◽  
Wave Functions ◽  
Quantum Mechanical ◽  
One Dimensional ◽  
Erwin Schrödinger ◽  
The One ◽  
Over Time

The father of quantum mechanics, Erwin Schrodinger, was one of the most important figures in the development of quantum theory. He is perhaps best known for his contribution of the wave equation, which would later result in his winning of the Nobel Prize for Physics in 1933. The Schrodinger wave equation describes the quantum mechanical behaviour of particles and explores how the Schrodinger wave functions of a system change over time. This project is concerned about exploring the one-dimensional case of the Schrodinger wave equation in a harmonic oscillator system. We will give the solutions, called eigenfunctions, of the equation that satisfy certain conditions. Furthermore, we will show that this happens only for particular values called eigenvalues.

scholarly journals INSTANTON CALCULATION OF THE DENSITY OF STATES OF DISORDERED PEIERLS CHAINS

1999 ◽  
Vol 13 (13) ◽  
pp. 1601-1618 ◽  
Author(s):  
MAXIM MOSTOVOY ◽  
JASPER KNOESTER
Keyword(s):  
Density Of States ◽  
Quantum Mechanical ◽  
Gap Model ◽  
Electron States ◽  
One Dimensional ◽  
Fluctuation Method ◽  
The One ◽  
Varying Mass ◽  
Density Of Electron States ◽  
Dirac Hamiltonian

We use the optimal fluctuation method to find the density of electron states inside the pseudogap in disordered Peierls chains. The electrons are described by the one-dimensional Dirac Hamiltonian with randomly varying mass (the Fluctuating Gap Model). We establish a relation between the disorder average in this model and the quantum-mechanical average for a certain double-well problem. We show that the optimal disorder fluctuation, which has the form of a soliton–antisoliton pair, corresponds to the instanton trajectory in the double-well problem. We use the instanton method developed for the double-well problem to find the contribution to the density of states from disorder realizations close to the optimal fluctuation.

Thermal Vacuum Polarization Using the Quantum Mechanical Path Integral

1997 ◽  
Vol 12 (30) ◽  
pp. 5387-5396 ◽  
Author(s):  
D. G. C. Mckeon
Keyword(s):  
Path Integral ◽  
Vacuum Polarization ◽  
Thermal Field ◽  
Quantum Mechanical ◽  
Loop Order ◽  
Thermal Vacuum ◽  
One Dimensional ◽  
Loop Expansion ◽  
High Temperature Expansion ◽  
The One

It has been shown how the quantum mechanical path integral can be used to do perturbative calculations in both quantum and thermal field theory to any order of the loop expansion. However, it is not readily apparent how gauge invariance is made manifest in this approach; in this paper we demonstrate how the vacuum polarization in electrodynamics at one-loop order is in fact transverse. We employ the one-dimensional Green's function [Formula: see text] in conjunction with an integration-by-parts procedure akin to that used by Strassler and Bern and Kosower. Surface terms in this approach are all zero. We obtain the high temperature expansion for the vacuum polarization in the static limit.

NOISE AND CORRELATED TRANSPORT IN ION CHANNELS

2004 ◽  
Vol 04 (01) ◽  
pp. L171-L178 ◽  
Author(s):  
H. HAKEN
Keyword(s):  
Occupation Number ◽  
Rate Equations ◽  
Quantum Mechanical ◽  
Transition Rates ◽  
Operator Equations ◽  
Occupation Numbers ◽  
Classical Quantum ◽  
The Individual ◽  
Quantum Mechanical Operator ◽  
Mechanical Operator

The motion of an ion through a channel is described as a classical/quantum mechanical hopping process between the individual sites of a channel. The transition rates are due to the coupling of an ion to suitable reservoirs. If fluctuating forces are added to the rate equations for the occupation numbers, the equations become quantum mechanical operator equations. Using previous results, the fluctuating forces are uniquely determined by the requirement of quantum mechanical consistency. The resulting equations are solved for several cases and the occupation number fluctuations discussed. Particular emphasis is laid on a model of correlated transport.

Sign in / Sign up

Export Citation Format

Share Document