On a relation of pseudoanalytic function theory to the two-dimensional stationary Schrödinger equation and Taylor series in formal powers for its solutions

Vladislav V Kravchenko

doi:10.1088/0305-4470/38/18/006

On a relation of pseudoanalytic function theory to the two-dimensional stationary Schrödinger equation and Taylor series in formal powers for its solutions

Journal of Physics A General Physics ◽

10.1088/0305-4470/38/18/006 ◽

2005 ◽

Vol 38 (18) ◽

pp. 3947-3964 ◽

Cited By ~ 27

Author(s):

Vladislav V Kravchenko

Keyword(s):

Schrödinger Equation ◽

Taylor Series ◽

Schrodinger Equation ◽

Function Theory ◽

Two Dimensional ◽

Stationary Schrödinger Equation ◽

Pseudoanalytic Function

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On the reduction of the multidimensional stationary Schrödinger equation to a first-order equation and its relation to the pseudoanalytic function theory

Journal of Physics A General Physics ◽

10.1088/0305-4470/38/4/006 ◽

2005 ◽

Vol 38 (4) ◽

pp. 851-868 ◽

Cited By ~ 16

Author(s):

Vladislav V Kravchenko

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Function Theory ◽

Order Equation ◽

Stationary Schrödinger Equation ◽

First Order ◽

Pseudoanalytic Function

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On a relation of bicomplex pseudoanalytic function theory to the complexified stationary Schrödinger equation

Complex Variables and Elliptic Equations ◽

10.1080/17476930701769058 ◽

2008 ◽

Vol 53 (6) ◽

pp. 501-521 ◽

Cited By ~ 11

Author(s):

D. Rochon

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Function Theory ◽

Stationary Schrödinger Equation ◽

Pseudoanalytic Function

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New lumps of Veselov–Novikov integrable nonlinear equation and new exact rational potentials of two-dimensional stationary Schrödinger equation via -dressing method

Physics Letters A ◽

10.1016/s0375-9601(03)00715-1 ◽

2003 ◽

Vol 313 (1-2) ◽

pp. 68-76 ◽

Cited By ~ 9

Author(s):

V.G. Dubrovsky ◽

I.B. Formusatik

Keyword(s):

Schrödinger Equation ◽

Nonlinear Equation ◽

Schrodinger Equation ◽

Two Dimensional ◽

Stationary Schrödinger Equation ◽

Dressing Method ◽

Integrable Nonlinear Equation

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Erratum: “On square-integrability of solutions of the stationary Schrödinger equation for the quantum harmonic oscillator in two dimensional constant curvature spaces” [J. Math. Phys. 56, 072101 (2015)]

Journal of Mathematical Physics ◽

10.1063/1.4929846 ◽

2015 ◽

Vol 56 (8) ◽

pp. 089901

Author(s):

Norman Noguera ◽

Krzysztof Rózga

Keyword(s):

Schrödinger Equation ◽

Harmonic Oscillator ◽

Constant Curvature ◽

Schrodinger Equation ◽

Two Dimensional ◽

Quantum Harmonic Oscillator ◽

Stationary Schrödinger Equation ◽

Square Integrability ◽

Math Phys ◽

Constant Curvature Spaces

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On square-integrability of solutions of the stationary Schrödinger equation for the quantum harmonic oscillator in two dimensional constant curvature spaces

Journal of Mathematical Physics ◽

10.1063/1.4922813 ◽

2015 ◽

Vol 56 (7) ◽

pp. 072101 ◽

Cited By ~ 1

Author(s):

Norman Noguera ◽

Krzysztof Rózga

Keyword(s):

Schrödinger Equation ◽

Harmonic Oscillator ◽

Constant Curvature ◽

Schrodinger Equation ◽

Two Dimensional ◽

Quantum Harmonic Oscillator ◽

Stationary Schrödinger Equation ◽

Square Integrability ◽

Constant Curvature Spaces

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On the two-dimensional stationary Schrödinger equation with a singular potential

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2010.11.004 ◽

2011 ◽

Vol 377 (1) ◽

pp. 420-427 ◽

Cited By ~ 2

Author(s):

Vladislav V. Kravchenko ◽

Abdelhamid Meziani

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Singular Potential ◽

Two Dimensional ◽

Stationary Schrödinger Equation

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Nonlocal Darboux transformation of the two-dimensional stationary Schrödinger equation and its relation to the Moutard transformation

Theoretical and Mathematical Physics ◽

10.1134/s0040577916040024 ◽

2016 ◽

Vol 187 (1) ◽

pp. 455-462 ◽

Cited By ~ 2

Author(s):

A. G. Kudryavtsev

Keyword(s):

Schrödinger Equation ◽

Darboux Transformation ◽

Schrodinger Equation ◽

Two Dimensional ◽

Stationary Schrödinger Equation ◽

Moutard Transformation

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New rational solutions of Veselov-Novikov equation and new exact rational potentials of two-dimensional stationary Schrodinger equation via ∂/sup ~/-dressing method

Proceedings. The 9th Russian-Korean International Symposium on Science and Technology, 2005. KORUS 2005. ◽

10.1109/korus.2005.1507665 ◽

2006 ◽

Author(s):

V.G. Dubrovsky ◽

I.B. Formusatik

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Two Dimensional ◽

Rational Solutions ◽

Stationary Schrödinger Equation ◽

Dressing Method ◽

Novikov Equation

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Solution of the two-dimensional stationary schrödinger equation with cosine-like coefficient (in view of X-ray diffraction)

phys stat sol (a) ◽

10.1002/pssa.2211050205 ◽

1988 ◽

Vol 105 (2) ◽

pp. 345-355 ◽

Cited By ~ 13

Author(s):

A. P. Beezirganyan ◽

P. A. Bezirganyan

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Two Dimensional ◽

X Ray Diffraction ◽

Stationary Schrödinger Equation ◽

X Ray

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Two-dimensional stationary Schrödinger equation via the ∂¯-dressing method: New exactly solvable potentials, wave functions, and their physical interpretation

Journal of Mathematical Physics ◽

10.1063/1.3484162 ◽

2010 ◽

Vol 51 (9) ◽

pp. 092106 ◽

Cited By ~ 2

Author(s):

V. G. Dubrovsky ◽

A. V. Topovsky ◽

M. Yu. Basalaev

Keyword(s):

Schrödinger Equation ◽

Physical Interpretation ◽

Schrodinger Equation ◽

Wave Functions ◽

Two Dimensional ◽

Stationary Schrödinger Equation ◽

Dressing Method ◽

Solvable Potentials ◽

Exactly Solvable Potentials ◽

Exactly Solvable

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