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  1. 5 Open Physics

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  1. 5 Schulze-Halberg A.

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1
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Darboux operators for linear first-order multi-component equations in arbitrary dimensions

100%
Schulze-Halberg A.
Open Physics
|
2013
|
vol. 11
|
issue 4
457-469
EN
We construct Darboux operators for linear, multi-component partial differential equations of first order. The number of variables and the dimension of the matrix coefficients in our equations are arbitrary. The Darboux operator and the transformed equation are worked out explicitly. We present an application of our formalism to the (1+2)-dimensional Weyl equation.
2
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Exact quantization formula for affine linearly energy-dependent potentials

100%
Schulze-Halberg A.
Open Physics
|
2011
|
vol. 9
|
issue 1
57-64
EN
We construct an exact quantization formula for Schrödinger equations with potentials thatdepend affine linearly on the energy, that is, they contain a term linear in the energy plus an energy-independent term. If such an energy-dependent potential admits a discrete spectrum and its ground state solution is known, our formula predicts the complete energy spectrum in exact form.
3
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Generalized linear Schrödinger equations and their Darboux transformations

100%
Schulze-Halberg A.
Open Physics
|
2008
|
vol. 6
|
issue 3
654-661
EN
We construct explicit Darboux transformations of arbitrary order for a class of generalized, linear Schrödinger equations. Our construction contains the well-known Darboux transformations for Schrödinger equations with position-dependent mass, Schrödinger equations coupled to a vector potential and Schrödinger equations for weighted energy.
4
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Quantum systems with effective and time-dependent masses: form-preserving transformations and reality conditions

100%
Schulze-Halberg A.
Open Physics
|
2005
|
vol. 3
|
issue 4
591-609
EN
We study the time-dependent Schrödinger equation (TDSE) with an effective (position-dependent) mass, relevant in the context of transport phenomena in semiconductors. The most general form-preserving transformation between two TDSEs with different effective masses is derived. A condition guaranteeing the reality of the potential in the transformed TDSE is obtained. To ensure maximal generality, the mass in the TDSE is allowed to depend on time also.
5
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Supersymmetry of time-dependent Schrödinger equations with effective mass

100%
Schulze-Halberg A.
|
EN
We establish the supersymmetry formalism for time-dependent Schrödinger equations with effective mass and show that the corresponding supersymmetric transformations are equivalent to effective mass Darboux transformations
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