scholarly journals Circuit Simulates One-Dimensional Quantum System

Physics ◽  
2018 ◽  
Vol 11 ◽  
Author(s):  
Emanuele Dalla Torre ◽  
Eran Sela
Keyword(s):  
Quantum System ◽  
One Dimensional

Quantum Boxes, Stringed Instruments

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Energy Level ◽  
Schrödinger Equation ◽  
Quantum System ◽  
Schrodinger Equation ◽  
Probability Distributions ◽  
Wave Functions ◽  
Energy Level Diagram ◽  
One Dimensional ◽  
Stringed Instruments ◽  
Symmetry Properties

Chapter 7 illustrates the results obtained by applying the Schrödinger equation to a simple pedagogical quantum system, the particle in a one-dimensional box. The wave functions are seen to be sine waves; their wavelengths are evaluated and used to calculate the quantized energies via the de Broglie relation. An energy-level diagram of some of the energies is constructed; on it are illustrations of the corresponding wave functions and probability distributions. The wave functions are seen to be either symmetric or antisymmetric about the midpoint of the line representing the box, thereby providing a lead-in to the later exploration of certain symmetry properties of multi-electron atoms. It is next pointed out that the Schrödinger equation for this system is identical to Newton’s equation describing the vibrations of a stretched musical string. The different meaning of the two solutions is discussed, as is the concept and structure of linear superpositions of them.

BACKSCATTERING AND THE DECAY OF TRANSMITTANCE IN A COHERENTLY ABSORBING OR AMPLIFYING ORDERED CHAIN

1996 ◽  
Vol 10 (03n05) ◽  
pp. 125-132 ◽  
Author(s):  
ASOK K. SEN
Keyword(s):  
Quantum System ◽  
Electronic Properties ◽  
Recent Work ◽  
Active Medium ◽  
Open Quantum System ◽  
Tight Binding ◽  
One Dimensional ◽  
A Value ◽  
Closed Quantum System ◽  
Coherent Amplification

We study electronic properties of a one-dimensional, semi-infinite ordered chain in the presence of either absorption or amplification at each site (the site potentials having imaginary positive or negative parts) within a single-band, tight binding Hamiltonian. The spectrum in either case for an isolated (closed) quantum system becomes broader compared to the regular Bloch case. For an infinitely long ordered chain (open quantum system), the reflectance saturates to a value greater (lesser) than unity in the amplifying (absorbing) case and the transmittance decays to zero in either case. Thus, in contrast to a recent work of Pradhan and Kumar [Phys. Rev.B50, 9644 (1994)], it is not necessary to have any “synergy between wave confinement” due to any disorder or interaction induced confining mechanism on the transmitted wave and “coherent amplification by the active medium” to achieve an amplification in the reflectance.

scholarly journals Chaos in a one-dimensional integrable quantum system

2009 ◽  
Vol 373 (8-9) ◽  
pp. 826-831 ◽  
Author(s):  
Petr Šeba ◽  
Daniel Vašata
Keyword(s):  
Quantum System ◽  
One Dimensional ◽  
Integrable Quantum

QUANTUM HAMILTONIANS AND SELF-ORGANISED CRITICALITY

1994 ◽  
Vol 08 (25n26) ◽  
pp. 3463-3471 ◽  
Author(s):  
JOHN CARDY
Keyword(s):  
Master Equation ◽  
Quantum System ◽  
Critical Behavior ◽  
Classical Limit ◽  
Particle Model ◽  
Hydrodynamic Behavior ◽  
One Dimensional ◽  
Self Organised Criticality ◽  
Stochastic Particle

We consider a stochastic particle model which has been proposed to exhibit the essential features of self-organised criticality. The master equation is reformulated as a one-dimensional quantum system of interacting bosons. The hydrodynamic behavior of the system is recovered as the classical limit of the quantum system, and the problem of fluctuations, important for the critical behavior, is discussed.

On the solution of an equation occurring in quantum mechanics

1965 ◽  
Vol 61 (2) ◽  
pp. 535-536
Author(s):  
M. Anthea Grubb
Keyword(s):  
Quantum Mechanics ◽  
Quantum System ◽  
Exponential Decay ◽  
One Dimensional ◽  
Exponential Decay Law ◽  
Image Position

The following equation arose in a study of the evolution of a one-dimensional quantum system:where α and κ are positive constants, andIt will be shown that this system provides an example of exactly exponential decay. This is of interest in view of recent papers discussing the validity of the exponential decay law (see, for example, Khalfin (1)and Martin (2)).

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