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pdf:docinfo:title: The Laplace Method for Energy Eigenvalue Problems in Quantum Mechanics
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Keywords: nonrelativistic quantum mechanics; exactly solvable problems; Laplace method
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subject: Quantum mechanics has about a dozen exactly solvable potentials. Normally, the time-independent Schrödinger equation for them is solved by using a generalized series solution for the bound states (using the Fröbenius method) and then an analytic continuation for the continuum states (if present). In this work, we present an alternative way to solve these problems, based on the Laplace method. This technique uses a similar procedure for the bound states and for the continuum states. It was originally used by Schrödinger when he solved the wave functions of hydrogen. Dirac advocated using this method too. We discuss why it is a powerful approach to solve all problems whose wave functions are represented in terms of confluent hypergeometric functions, especially for the continuum solutions, which can be determined by an easy-to-program contour integral.
dc:creator: Jeremy Canfield, Anna Galler and James K. Freericks
dcterms:created: 2023-04-20T13:21:29Z
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title: The Laplace Method for Energy Eigenvalue Problems in Quantum Mechanics
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pdf:docinfo:keywords: nonrelativistic quantum mechanics; exactly solvable problems; Laplace method
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dc:title: The Laplace Method for Energy Eigenvalue Problems in Quantum Mechanics
modified: 2023-04-20T13:23:32Z
cp:subject: Quantum mechanics has about a dozen exactly solvable potentials. Normally, the time-independent Schrödinger equation for them is solved by using a generalized series solution for the bound states (using the Fröbenius method) and then an analytic continuation for the continuum states (if present). In this work, we present an alternative way to solve these problems, based on the Laplace method. This technique uses a similar procedure for the bound states and for the continuum states. It was originally used by Schrödinger when he solved the wave functions of hydrogen. Dirac advocated using this method too. We discuss why it is a powerful approach to solve all problems whose wave functions are represented in terms of confluent hypergeometric functions, especially for the continuum solutions, which can be determined by an easy-to-program contour integral.
pdf:docinfo:subject: Quantum mechanics has about a dozen exactly solvable potentials. Normally, the time-independent Schrödinger equation for them is solved by using a generalized series solution for the bound states (using the Fröbenius method) and then an analytic continuation for the continuum states (if present). In this work, we present an alternative way to solve these problems, based on the Laplace method. This technique uses a similar procedure for the bound states and for the continuum states. It was originally used by Schrödinger when he solved the wave functions of hydrogen. Dirac advocated using this method too. We discuss why it is a powerful approach to solve all problems whose wave functions are represented in terms of confluent hypergeometric functions, especially for the continuum solutions, which can be determined by an easy-to-program contour integral.
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pdf:docinfo:creator: Jeremy Canfield, Anna Galler and James K. Freericks
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creator: Jeremy Canfield, Anna Galler and James K. Freericks
meta:author: Jeremy Canfield, Anna Galler and James K. Freericks
dc:subject: nonrelativistic quantum mechanics; exactly solvable problems; Laplace method
meta:creation-date: 2023-04-20T13:21:29Z
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Author: Jeremy Canfield, Anna Galler and James K. Freericks
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