# On form-preserving transformations for the time-dependent Schrödinger equation

@article{Finkel1998OnFT, title={On form-preserving transformations for the time-dependent Schr{\"o}dinger equation}, author={Federico Finkel and Artemio Gonz{\'a}lez-L{\'o}pez and Niky Kamran and Miguel A. Rodriguez}, journal={Journal of Mathematical Physics}, year={1998}, volume={40}, pages={3268-3274} }

In this paper we point out a close connection between the Darboux transformation and the group of point transformations which preserve the form of the time-dependent Schrodinger equation (TDSE). In our main result, we prove that any pair of time-dependent real potentials related by a Darboux transformation for the TDSE may be transformed by a suitable point transformation into a pair of time-independent potentials related by a usual Darboux transformation for the stationary Schrodinger equation…

## 34 Citations

### Form-preserving Transformations for the Time-dependent Schrödinger Equation in (n + 1) Dimensions

- Mathematics
- 2006

We define a form-preserving transformation (also called point canonical transformation) for the time-dependent Schrödinger equation (TDSE) in (n+1) dimensions. The form-preserving transformation is…

### Point Transformations: Exact Solutions of the Quantum Time-Dependent Mass Nonstationary Oscillator

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In this note we address the exact solutions of a time-dependent Hamiltonian composed by an oscillator-like interaction with both a frequency and a mass term that depend on time. The latter is…

### Form-Preserving Transformations of Time-Dependent Schrodinger Equation with Time- and Position-Dependent Mass

- Physics
- 2005

We study space-time transformations of the time-dependent Schr?dinger equation (TDSE) with time- and position-dependent (effective) mass. We obtain the most general space-time transformation that…

### EFFECTIVE MASS HAMILTONIANS WITH LINEAR TERMS IN THE MOMENTUM: DARBOUX TRANSFORMATIONS AND FORM-PRESERVING TRANSFORMATIONS

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- 2007

We define form-preserving transformations and Darboux transformations for time-dependent, effective mass Hamiltonians with additional linear terms. We give reality conditions for both…

### Reduction of Time-Dependent Schrödinger Equations with Effective Mass to Stationary Schrödinger Equations

- Physics, Mathematics
- 2008

Schrodinger equations with effective mass occur in the context of transport phenomena in crystals (e.g., semiconductors), where the electrons are not completely free, but interact with the potential…

### Fourth Painlevé and Ermakov equations: quantum invariants and new exactly-solvable time-dependent Hamiltonians

- Mathematics, PhysicsJournal of Physics A: Mathematical and Theoretical
- 2020

In this work, we introduce a new realization of exactly-solvable time-dependent Hamiltonians based on the solutions of the fourth Painlevé and the Ermakov equations. The latter is achieved by…

### DARBOUX TRANSFORMATIONS FOR TIME-DEPENDENT SCHRÖDINGER EQUATIONS WITH EFFECTIVE MASS

- Physics, Mathematics
- 2006

The formalism of Darboux transformations is established for time-dependent Schrodinger equations with an effective (position-dependent) mass. Explicit formulas are obtained for the transformed wave…

### Quantum systems with effective and time-dependent masses: form-preserving transformations and reality conditions

- Physics
- 2005

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…

### A new type of Darboux transformations for the one-dimensional Burgers equation with forcing

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- 2021

We construct new types of arbitrary-order Darboux transformations for the stationary forced Burgers equation in one dimension. The distinguishing property of these transformations is that they…

### Form-Preserving Transformations for Hamiltonians with Linear Terms in the Momentum

- Physics
- 2005

No HeadingWe consider Hamiltonians in (1+1) dimensions that contain linear terms in the momentum, resembling systems under the influence of a vector potential. For the time-dependent Schrödinger…

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