PHASE RIGIDITY OF POINT INTERACTIONS

2012 ◽  
Vol 27 (01) ◽  
pp. 1350001 ◽  
Author(s):  
S. Lj. S. KOČINAC ◽  
V. MILANOVIĆ
Keyword(s):  
Quantum Mechanics ◽  
Bound States ◽  
Point Interaction ◽  
Supersymmetric Quantum Mechanics ◽  
Point Interactions ◽  
One Dimensional ◽  
Generate Family ◽  
Discrete Part ◽  
The Continuum

In this paper, we investigate phase rigidity of one-dimensional point interactions. With the aid of supersymmetric quantum mechanics (SUSYQM) we generate family of isospectral potentials describing point interactions. We than demonstrate that for SUSYQM generated bound states in the continuum (BIC) phase rigidity is always zero, while for bound states from discrete part of spectrum phase rigidity may vary from zero to unity, depending on the strength of point interaction.

BOUND STATES IN CONTINUUM GENERATED BY POINT INTERACTION AND SUPERSYMMETRIC QUANTUM MECHANICS

2012 ◽  
Vol 26 (27) ◽  
pp. 1250177 ◽  
Author(s):  
S. Lj. S. KOČINAC ◽  
V. MILANOVIĆ
Keyword(s):  
Quantum Mechanics ◽  
Kinetic Energy ◽  
Bound States ◽  
Energy Operator ◽  
Bound State ◽  
Point Interaction ◽  
Supersymmetric Quantum Mechanics ◽  
Kinetic Energy Operator ◽  
Point Interactions ◽  
The Continuum

Four-parameter family of point interactions represent all possible self-adjoint extensions of kinetic energy operator. We demonstrate a method for generating a bound state in the continuum of point interactions which relies on supersymmetric quantum mechanics (SUSYQM). Both zero and nonzero transparency cases are considered.

scholarly journals Bound states in the continuum from supersymmetric quantum mechanics

1993 ◽  
Vol 48 (5) ◽  
pp. 3525-3531 ◽  
Author(s):  
J. Pappademos ◽  
U. Sukhatme ◽  
A. Pagnamenta
Keyword(s):  
Quantum Mechanics ◽  
Bound States ◽  
Supersymmetric Quantum Mechanics ◽  
The Continuum

scholarly journals One-dimensional photonic bound states in the continuum

2020 ◽  
Vol 3 (1) ◽  
Author(s):  
P. S. Pankin ◽  
B.-R. Wu ◽  
J.-H. Yang ◽  
K.-P. Chen ◽  
I. V. Timofeev ◽  
...  
Keyword(s):  
Bound States ◽  
One Dimensional ◽  
The Continuum

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 Bound states at threshold in supersymmetric quantum mechanics

1998 ◽  
Vol 515 (1-2) ◽  
pp. 184-202 ◽  
Author(s):  
Massimo Porrati ◽  
Alexander Rozenberg
Keyword(s):  
Quantum Mechanics ◽  
Bound States ◽  
Supersymmetric Quantum Mechanics
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