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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Non-deformed singular and non-singular exponential-type potentials.

J J Pe Na1, G Ovando2, J Morales2

  • 1Universidad Autónoma Metropolitana - Azc., DCB, Area de Física Atómica Molecular Aplicada, San Pablo 180, Mexico City, 02200, Mexico. jjpg@correo.azc.uam.mx.

Journal of Molecular Modeling
|August 20, 2017
PubMed
Summary
This summary is machine-generated.

A new method transforms the Schrödinger equation into a hypergeometric-type equation, yielding exactly solvable multiparameter exponential-type (ME-T) potentials. This approach unifies various quantum potential models and identifies their singular/non-singular partners.

Keywords:
Canonical transformationExponential-type potentialsSchrödinger and hypergeometric DE

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Area of Science:

  • Quantum Mechanics
  • Mathematical Physics

Background:

  • The Schrödinger equation is central to quantum mechanics.
  • Solving the Schrödinger equation for various potential models often requires specialized methods.
  • Understanding potential models is crucial for studying molecular electronic properties.

Purpose of the Study:

  • To present a unified method for solving the Schrödinger equation for a wide range of quantum potentials.
  • To obtain exactly solvable multiparameter exponential-type (ME-T) potentials and their corresponding wavefunctions.
  • To identify relationships between different potential models and their physical properties.

Main Methods:

  • Application of the canonical transformation method to the Schrödinger equation.
  • Transformation into a second-order differential equation of hypergeometric-type.
  • Analysis of parameters within the ME-T potential framework.

Main Results:

  • Derivation of exactly solvable ME-T potentials with hypergeometric wavefunctions.
  • Identification of families of radial (singular) and one-dimensional (non-singular) potentials.
  • Demonstration that specific parameter choices yield known deformed and non-deformed potential models.
  • Establishment of conditions for the existence of singular/non-singular potential partners.

Conclusions:

  • The canonical transformation method offers a unified approach to solving the Schrödinger equation for diverse potential models.
  • This method simplifies the identification of potential types and their partners.
  • New quantum potentials are generated, offering alternatives for quantum applications.