scholarly journals TRANSMISSION PROPERTIES OF THE ONE-DIMENSIONAL ARRAY OF DELTA POTENTIALS

2011 ◽  
Vol 25 (16) ◽  
pp. 1349-1358 ◽  
Author(s):  
GUILLERMO CORDOURIER-MARURI ◽  
ROMEO DE COSS ◽  
VIRENDRA GUPTA
Keyword(s):  
Linear Array ◽  
Delta Function ◽  
Transmission Probability ◽  
Quantum Waveguide ◽  
One Dimensional ◽  
Transmission Properties ◽  
Moving Particle ◽  
The One ◽  
Regular Arrays ◽  
Function Potential

The problem of one-dimensional quantum wire along which a moving particle interacts with a linear array of N delta-function potentials is studied. Using a quantum waveguide approach, the transfer matrix is calculated to obtain the transmission probability of the particle. Results for arbitrary N and for specific regular arrays are presented. Some particular symmetries and invariances of the delta-function potential array for the N = 2 case are analyzed in detail. It is shown that perfect transmission can take place in a variety of situations.

QUANTUM TRANSPORT IN MESOSCOPIC RINGS WITH STUBS

1996 ◽  
Vol 10 (26) ◽  
pp. 3569-3581 ◽  
Author(s):  
SAM YOUNG CHO ◽  
TAESEUNG CHOI ◽  
CHANG-MO RYU
Keyword(s):  
Quantum Transport ◽  
Transmission Probability ◽  
Localized States ◽  
Persistent Currents ◽  
Quantum Waveguide ◽  
One Dimensional ◽  
Continuum States ◽  
Discrete States ◽  
The One ◽  
The Continuum

Quantum transport in the open-system mesoscopic rings with stubs in the absence of magnetic field is investigated by using the one-dimensional quantum waveguide theory. It is shown that discretely localized states due to the presence of stubs play an important role in the electron transport. The behavior of transmission probability shows the asymmetric Fano resonance, which arises from the interaction between the continuum states and the discrete states. Amplification of the persistent currents by the localized states due to the stub is clearly shown. Negative currents are also noticed.

scholarly journals FERMIONIC DUAL OF ONE-DIMENSIONAL BOSONIC PARTICLES WITH DERIVATIVE DELTA FUNCTION POTENTIAL

2010 ◽  
Vol 25 (09) ◽  
pp. 715-725
Author(s):  
B. BASU-MALLICK ◽  
TANAYA BHATTACHARYYA
Keyword(s):  
Center Of Mass ◽  
Delta Function ◽  
Bose Gas ◽  
Duality Relation ◽  
Coupling Constant ◽  
Range Interaction ◽  
Fermionic System ◽  
One Dimensional ◽  
Zero Range ◽  
Function Potential

We investigate the boson–fermion duality relation for the case of quantum integrable derivative δ-function Bose gas. In particular, we find a dual fermionic system with nonvanishing zero-range interaction for the simplest case of two bosonic particles with derivative δ-function interaction. The coupling constant of this dual fermionic system becomes inversely proportional to the product of the coupling constant of its bosonic counterpart and the center-of-mass momentum of the corresponding eigenfunction.

QUANTUM WAVEGUIDE THEORY FOR TRIPLY CONNECTED AHARONOV–BOHM RINGS

1996 ◽  
Vol 10 (06) ◽  
pp. 701-712 ◽  
Author(s):  
CHANG-MO RYU ◽  
SAM YOUNG CHO ◽  
MINCHEOL SHIN ◽  
KYOUNG WAN PARK ◽  
SEONGJAE LEE ◽  
...  
Keyword(s):  
Magnetic Flux ◽  
Wave Vector ◽  
Quantum Interference ◽  
Transmission Probability ◽  
Interference Effects ◽  
Quantum Waveguide ◽  
One Dimensional ◽  
Waveguide Theory ◽  
Aharonov Bohm ◽  
Transmission And Reflection

Quantum interference effects for a mesoscopic loop with three leads are investigated by using a one-dimensional quantum waveguide theory. The transmission and reflection probabilities are analytically obtained in terms of the magnetic flux, arm length, and wave vector. Oscillation of the magnetoconductance is explicitly demonstrated. Magnetoconductance is found to be sharply peaked for certain localized values of flux and kl. In addition, it is noticed that the periodicity of the transmission probability with respect to kl depends more sensitively on the lead position, compared to the case of the two-lead loop.

scholarly journals Variational approach to the Schrödinger equation with a delta-function potential

2021 ◽  
Author(s):  
Francisco Marcelo Fernandez
Keyword(s):  
Variational Method ◽  
Delta Function ◽  
Basis Set ◽  
One Dimensional ◽  
Dirac Delta ◽  
Introductory Course ◽  
Relevant Role ◽  
Secular Equations ◽  
The One ◽  
Computer Algebra Software

Abstract We obtain accurate eigenvalues of the one-dimensional Schr\"{o}dinger equation with a Hamiltonian of the form $H_{g}=H+g\delta (x)$, where $\delta (x)$ is the Dirac delta function. We show that the well known Rayleigh-Ritz variational method is a suitable approach provided that the basis set takes into account the effect of the Dirac delta on the wavefunction. Present analysis may be suitable for an introductory course on quantum mechanics to illustrate the application of the Rayleigh-Ritz variational method to a problem where the boundary conditions play a relevant role and have to be introduced carefully into the trial function. Besides, the examples are suitable for motivating the students to resort to any computer-algebra software in order to calculate the required integrals and solve the secular equations.

scholarly journals Generalized Continuity Equation for Quasi-Hermitian Hamiltonians

10.14311/1803 ◽  
2013 ◽  
Vol 53 (3) ◽  
Author(s):  
Amine B. Hammou
Keyword(s):  
Continuity Equation ◽  
Delta Function ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
One Dimensional ◽  
Transmission Coefficients ◽  
Generalized Continuity ◽  
Unitarity Relation ◽  
Function Potential

The continuity relation is generalized to quasi-Hermitian one-dimensional Hamiltonians. As an application we show that the reflection and transmission coefficients computed with the generalized current obey the conventional unitarity relation for the continuous double delta function potential.

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