Bound states emerging from below the continuum in a solvablePT-symmetric discrete Schrödinger equation

Physical Review A ◽

10.1103/physreva.96.012127 ◽

2017 ◽

Vol 96 (1) ◽

Author(s):

Miloslav Znojil

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Bound States ◽

Discrete Schrödinger Equation ◽

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The criterion of absence of bound states in two-dimensional perturbation of the discrete Schrodinger equation

2017 Days on Diffraction (DD) ◽

10.1109/dd.2017.8167998 ◽

2017 ◽

Author(s):

V.V. Borzov ◽

E.V. Damaskinsky

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Bound States ◽

Two Dimensional ◽

Discrete Schrödinger Equation

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The transition of energy and bound states in the continuum of fractional Schrödinger equation in gravitational field and the effect of the minimal length

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2018.05.002 ◽

2019 ◽

Vol 67 ◽

pp. 290-302 ◽

Author(s):

Xiao Zhang ◽

Bo Yang ◽

Chaozhen Wei ◽

Maokang Luo

Keyword(s):

Gravitational Field ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Bound States ◽

Minimal Length ◽

Fractional Schrödinger Equation ◽

Fractional Schrodinger Equation ◽

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Bounded solution structure of Schrödinger equation in the presence of the minimal length and its effect: bound states in the continuum are universal

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2021.105694 ◽

2021 ◽

pp. 105694

Author(s):

Zhang Xiao ◽

Yang Bo ◽

Wei Chaozhen ◽

Luo Maokang

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Bound States ◽

Solution Structure ◽

Bounded Solution ◽

Minimal Length ◽

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Existence of solitary waves for the discrete Schrödinger equation coupled to a nonlinear oscillator

Russian Journal of Mathematical Physics ◽

10.1134/s1061920808040067 ◽

2008 ◽

Vol 15 (4) ◽

pp. 487-492 ◽

Author(s):

E. A. Kopylova

Keyword(s):

Schrödinger Equation ◽

Solitary Waves ◽

Schrodinger Equation ◽

Nonlinear Oscillator ◽

Discrete Schrödinger Equation

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Solution of the Schrödinger equation for bound states in closed form

Physical Review A ◽

10.1103/physreva.26.662 ◽

1982 ◽

Vol 26 (1) ◽

pp. 662-664 ◽

Author(s):

Edgardo Gerck ◽

Jason A. C. Gallas ◽

Augusto B. d'Oliveira

Keyword(s):

Schrödinger Equation ◽

Closed Form ◽

Schrodinger Equation ◽

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On the Bound States for the Three-Body Schrödinger Equation with Decaying Potentials

Few-Body Systems ◽

10.1007/s00601-012-0525-9 ◽

2013 ◽

Vol 54 (11) ◽

pp. 1799-1819

Author(s):

Rytis Juršėnas

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Bound States ◽

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Shallow Potential Wells for the Discrete Schrödinger Equation

Mathematical and Numerical Aspects of Wave Propagation WAVES 2003 ◽

10.1007/978-3-642-55856-6_139 ◽

2003 ◽

pp. 857-861

Author(s):

Joel A. Rodriguez-Ceballos ◽

Peter N. Zhevandrov

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Potential Wells ◽

Discrete Schrödinger Equation

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Dirichlet-to-Neumann and Neumann-to-Dirichlet embedding methods for bound states of the Schrödinger equation

Physical Review A ◽

10.1103/physreva.70.042103 ◽

2004 ◽

Vol 70 (4) ◽

Author(s):

Radosław Szmytkowski ◽

Sebastian Bielski

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Bound States ◽

Embedding Methods

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Bound states for two dimensional Schrödinger equation with anisotropic interactions localized on a circle

Journal of Mathematical Physics ◽

10.1063/1.4907382 ◽

2015 ◽

Vol 56 (2) ◽

pp. 022103 ◽

Author(s):

E. de Prunelé

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Bound States ◽

Two Dimensional ◽

Anisotropic Interactions

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A class of time periodic Hamiltonians with no bound states

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500021892 ◽

1987 ◽

Vol 105 (1) ◽

pp. 37-42

Author(s):

H. Kaneta

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Bound States ◽

All Solutions ◽

SynopsisWe generalise the Paley–Wiener closedness theorem and apply it to a class of time periodic Hamiltonians to show that all solutions to the corresponding Schrodinger equation decay.

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