Operator Calculus

Do Tan Si Xx

ISBN 10: 3659916021 / ISBN 13: 9783659916021

Verlag: LAP LAMBERT Academic Publishing Jul 2016, 2016

Beschreibung

Neuware -The operational calculus had the merit of introducing the notion of derivative operator but didn't help so much mathematics. Later, quantum mechanics introduced the position operator q linked to the derivative operator by a commutation relation. But q is not well adopted by mathematical analysis. This work proposes to reedify the operational calculus based on both derivative, position operators and a rule for the permutation of non commutative operators. Applcations for resolutions of differential equations , for obtaining operators that create by acting on monomials the polynomials most utilized in sciences and engineering. Their generating finctions, orthogonality and properties are then obtained in a coherent and very close way. This work shows also how, only from translation and Gaussian transform, to obtain the dilatation, the transform of x into real powers of x, the partial Fourier, Fourier, canonical transforms and how to get by them the transforms of arbitrary operators and functions, the related integral transform. The Laplace transform is also treated by the present method. Via the creation and the destruction operators applications in quantum mechanics are promisingBooks on Demand GmbH, Überseering 33, 22297 Hamburg 80 pp. Englisch.

Bestandsnummer des Verkäufers 9783659916021

Bibliografische Details

• Titel: Operator Calculus
• Verlag: LAP LAMBERT Academic Publishing Jul 2016
• Erscheinungsjahr: 2016
• Sprache: Englisch
• ISBN-10: 3659916021
• ISBN-13: 9783659916021
• Einband: Taschenbuch
• Zustand: Neu
• Abmessungen: 220B x 150 H x 5 T Millimeter Breite: 220 mm, Höhe: 150 mm, Tiefe: 5 mm
• Gewicht: 137 Gramm

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Inhaltsangabe

The operational calculus had the merit of introducing the notion of derivative operator but didn't help so much mathematics. Later, quantum mechanics introduced the position operator q linked to the derivative operator by a commutation relation. But q is not well adopted by mathematical analysis. This work proposes to reedify the operational calculus based on both derivative, position operators and a rule for the permutation of non commutative operators. Applcations for resolutions of differential equations , for obtaining operators that create by acting on monomials the polynomials most utilized in sciences and engineering. Their generating finctions, orthogonality and properties are then obtained in a coherent and very close way. This work shows also how, only from translation and Gaussian transform, to obtain the dilatation, the transform of x into real powers of x, the partial Fourier, Fourier, canonical transforms and how to get by them the transforms of arbitrary operators and functions, the related integral transform. The Laplace transform is also treated by the present method. Via the creation and the destruction operators applications in quantum mechanics are promising