Operator Calculus : Edification and Utilization

Do Tan Si Xx

ISBN 10: 3659916021 / ISBN 13: 9783659916021

Editore: LAP LAMBERT Academic Publishing, 2016

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nach der Bestellung gedruckt Neuware - Printed after ordering - 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.

Codice articolo 9783659916021

Dati bibliografici

• Titolo: Operator Calculus : Edification and Utilization
• Editore: LAP LAMBERT Academic Publishing
• Data di pubblicazione: 2016
• Lingua: Inglese
• ISBN 10: 3659916021
• ISBN 13: 9783659916021
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 220 L x 150 A x 5 P (millimetri) 220 millimetri di larghezza per 150 millimetri di altezza per 5 millimetri di profondità
• Peso: 137 grammi

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Riassunto

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