scholarly journals Leaky Modes of Waveguides as a Classical Optics Analogy of Quantum Resonances

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Sara Cruz y Cruz ◽  
Oscar Rosas-Ortiz
Keyword(s):  
Quantum Mechanics ◽  
Short Range ◽  
Bound States ◽  
Waveguide Structure ◽  
One Dimensional ◽  
Leaky Modes ◽  
Scattering States ◽  
Quantum Resonances ◽  
Zone Of Influence ◽  
Square Well

A classical optics waveguide structure is proposed to simulate resonances of short range one-dimensional potentials in quantum mechanics. The analogy is based on the well-known resemblance between the guided and radiation modes of a waveguide with the bound and scattering states of a quantum well. As resonances are scattering states that spend some time in the zone of influence of the scatterer, we associate them with the leaky modes of a waveguide, the latter characterized by suffering attenuation in the direction of propagation but increasing exponentially in the transverse directions. The resemblance is complete because resonances (leaky modes) can be interpreted as bound states (guided modes) with definite lifetime (longitudinal shift). As an immediate application we calculate the leaky modes (resonances) associated with a dielectric homogeneous slab (square well potential) and show that these modes are attenuated as they propagate.

WKB method for potentials unbounded from below

2016 ◽  
Vol 30 (03) ◽  
pp. 1650003 ◽  
Author(s):  
Aleksandar Demić ◽  
Vitomir Milanović ◽  
Jelena Radovanović ◽  
Milenko Musić
Keyword(s):  
Quantum Mechanics ◽  
Bound States ◽  
Wave Functions ◽  
Wkb Method ◽  
Symmetric Potential ◽  
Overlap Integral ◽  
Entire Spectrum ◽  
One Dimensional ◽  
Model Based ◽  
Exactly Solvable

Bound states degenerated in energy (and differing in parity) may form in one-dimensional quantum mechanics if the potential is unbounded from below. We focus on symmetric potential and present quasi-exactly solvable (QES) model based on WKB method. The application of this method is limited on slow-changing potentials. We consider the overlap integral of WKB wave functions [Formula: see text] and [Formula: see text] which correspond to energies [Formula: see text] and [Formula: see text], and by setting [Formula: see text], we determine the type of spectrum depending on parameter [Formula: see text] which arises from this method. For finite value [Formula: see text], we show that the entire spectrum will consist of degenerated bound states.

scholarly journals Dirac Particle for the Position Dependent Mass in the Generalized Asymmetric Woods-Saxon Potential

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Soner Alpdoğan ◽  
Ali Havare
Keyword(s):  
Bound States ◽  
Dirac Particle ◽  
Saxon Potential ◽  
One Dimensional ◽  
Transmission And Reflection Coefficients ◽  
Scattering States ◽  
Transmission Resonances ◽  
The One ◽  
Dependent Mass ◽  
Position Dependent Mass

The one-dimensional Dirac equation with position dependent mass in the generalized asymmetric Woods-Saxon potential is solved in terms of the hypergeometric functions. The transmission and reflection coefficients are obtained by considering the one-dimensional electric current density for the Dirac particle and the equation describing the bound states is found by utilizing the continuity conditions of the obtained wave function. Also, by using the generalized asymmetric Woods-Saxon potential solutions, the scattering states are found out without making calculation for the Woods-Saxon, Hulthen, cusp potentials, and so forth, which are derived from the generalized asymmetric Woods-Saxon potential and the conditions describing transmission resonances and supercriticality are achieved. At the same time, the data obtained in this work are compared with the results achieved in earlier studies and are observed to be consistent.

scholarly journals BOUND STATES OF THE KLEIN–GORDON EQUATION IN THE PRESENCE OF SHORT RANGE POTENTIALS

2006 ◽  
Vol 21 (02) ◽  
pp. 313-325 ◽  
Author(s):  
VÍCTOR M. VILLALBA ◽  
CLARA ROJAS
Keyword(s):  
Short Range ◽  
Bound States ◽  
Gordon Equation ◽  
Bound State ◽  
One Dimensional ◽  
Klein Gordon ◽  
Klein Gordon Equation

We solve the Klein–Gordon equation in the presence of a spatially one-dimensional cusp potential. The bound state solutions are derived and the antiparticle bound state is discussed.

ANOMALOUS SUSY QUANTUM MECHANICS, HETEROTIC MODELS AND SCATTERING STATES

1992 ◽  
Vol 07 (25) ◽  
pp. 2325-2331
Author(s):  
L. J. BOYA ◽  
J. CASAHORRÁN ◽  
J. G. ESTEVE
Keyword(s):  
Quantum Mechanics ◽  
Symmetry Breaking ◽  
Continuous Spectrum ◽  
Real Axis ◽  
Bound States ◽  
Anomalous Behavior ◽  
Heterotic String ◽  
Supersymmetric Quantum Mechanics ◽  
The Other ◽  
Scattering States

We analyze the symmetry breaking associated to anomalous realization of supersymmetry in the context of Supersymmetric Quantum Mechanics (SUSY QM). We show how the supercharge itself might become an anomalous operator in the process of quantization. We study a solvable potential in the Pöschl-Teller class containing both bound states and continuous spectrum. We find a situation reminiscent of the heterotic string: one of the two SUSY partners lives in the whole real axis while the other restricts itself to the half-line. Peculiarities of the model include negative energies, incomplete pairing of states and anomalous behavior for the phase shifts in scattering.

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