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New Potentials for Old: The Darboux Transformation in Quantum Mechanics

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Brian Wesley Williams

Department of Chemistry, Bucknell University, Lewisburg, PA 17837

Tevye C. Celius

Department of Chemistry and Biochemistry, Ohio Northern University, Ada, OH 45810

J. Chem. Educ., 2008, 85 (4), p 576

DOI: 10.1021/ed085p576

Publication Date (Web): April 1, 2008

Abstract

The Darboux transformation in quantum mechanics is reviewed at a basic level. Examples of how this transformation leads to exactly solvable potentials related to the "particle in a box" and the harmonic oscillator are shown in detail. The connection between the Darboux transformation and some modern operator based approaches to quantum mechanics is also outlined.

Keywords (Audience):

Graduate Education / Research

Keywords (Domain):

Physical Chemistry

Keywords (Pedagogy):

Textbooks / Reference Books

Keywords (Subject):

Quantum Chemistry

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Received: August 03, 2009

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Article

New Potentials for Old: The Darboux Transformation in Quantum Mechanics

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Keywords (Audience):

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SciFinder Links

History

Recommend & Share

Related Content

Determination of Phosphates by the Gravimetric Quimociac Technique

Bacterial Production of Poly(3-hydroxybutyrate). An Undergraduate Student Laboratory Experiment

The Use of Cyclic Voltammetry To Probe the Passivation of Electrode Surfaces by Well-Ordered Self-Assembly and Langmuir–Blodgett Films. An Advanced Undergraduate Laboratory Experiment in Surface Science and Nanomaterials Chemistry

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