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THE “SIMPLE” HARMONIC OSCILLATOR: AN INTRODUCTION TO THE MATHEMATICS OF QUANTUM MECHANICS

Gregory L. Naber

Jan 1, 20156 citations

Linear motion and the harmonic oscillator

Peter Joshua Atkins, Ronald Friedman

This chapter expresses the whole of quantum mechanics in terms of a small set of postulates, which embraces the behaviour of all known forms of matter. It introduces the postulates and illustrates how they are used, including how to apply them to problems of chemical interest, such as atomic and molecular structure and the properties of molecules. It also establishes the full significance of the Hψ=Eψequation and provides a foundation for its application. The chapter includes the solutions of the Schrödinger equation for a particle and the operator, which is a symbol for an instruction to carry out some action on a function. The principal mathematical difference between classical mechanics and quantum mechanics is that whereas in the former physical observables are represented by functions, in quantum mechanics they are represented by mathematical operators.This chapter expresses the whole of quantum mechanics in terms of a small set of postulates, which embraces the behaviour of all known forms of matter. It introduces the postulates and illustrates how they are used, including how to apply them to problems of chemical interest, such as atomic and molecular structure and the properties of molecules. It also establishes the full significance of the Hψ=Eψequation and provides a foundation for its application. The chapter includes the solutions of the Schrödinger equation for a particle and the operator, which is a symbol for an instruction to carry out some action on a function. The principal mathematical difference between classical mechanics and quantum mechanics is that whereas in the former physical observables are represented by functions, in quantum mechanics they are represented by mathematical operators.

Oxford University Press eBooksNov 11, 20101 citation

Harmonic oscillator in a variety of forms of classical and quantum mechanics

Petr Česnek

Jan 1, 20060 citations

Advanced Concepts in Quantum Mechanics

Giampiero V. M. Esposito, Giuseppe Marmo, Gennaro Miele +1 more

Introducing a geometric view of fundamental physics, starting from quantum mechanics and its experimental foundations, this book is ideal for advanced undergraduate and graduate students in quantum mechanics and mathematical physics. Focusing on structural issues and geometric ideas, this book guides readers from the concepts of classical mechanics to those of quantum mechanics. The book features an original presentation of classical mechanics, with the choice of topics motivated by the subsequent development of quantum mechanics, especially wave equations, Poisson brackets and harmonic oscillators. It also presents new treatments of waves and particles and the symmetries in quantum mechanics, as well as extensive coverage of the experimental foundations.Introducing a geometric view of fundamental physics, starting from quantum mechanics and its experimental foundations, this book is ideal for advanced undergraduate and graduate students in quantum mechanics and mathematical physics. Focusing on structural issues and geometric ideas, this book guides readers from the concepts of classical mechanics to those of quantum mechanics. The book features an original presentation of classical mechanics, with the choice of topics motivated by the subsequent development of quantum mechanics, especially wave equations, Poisson brackets and harmonic oscillators. It also presents new treatments of waves and particles and the symmetries in quantum mechanics, as well as extensive coverage of the experimental foundations.

Cambridge University Press eBooksOct 31, 201418 citations

The harmonic oscillator

Jeff Greensite

Written in a lucid and engaging style, the author takes readers from an overview of classical mechanics and the historical development of quantum theory through to advanced topics. The mathematical aspects of quantum theory necessary for a firm grasp of the subject are developed in the early chapters, but an effort is made to motivate that formalism on physical grounds. Including animated figures and their respective Mathematica® codes, this book provides a complete and comprehensive text for students in physics, maths, chemistry and engineering needing an accessible introduction to quantum mechanics. Supplementary Mathematica codes available within Book InformationWritten in a lucid and engaging style, the author takes readers from an overview of classical mechanics and the historical development of quantum theory through to advanced topics. The mathematical aspects of quantum theory necessary for a firm grasp of the subject are developed in the early chapters, but an effort is made to motivate that formalism on physical grounds. Including animated figures and their respective Mathematica® codes, this book provides a complete and comprehensive text for students in physics, maths, chemistry and engineering needing an accessible introduction to quantum mechanics. Supplementary Mathematica codes available within Book Information

Institute of Physics eBooksFeb 1, 20170 citations

1. Foundations of quantum mechanics

Guozhen Wu

De Gruyter eBooksApr 15, 20191,663 citations

The Harmonic Oscillator

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The Harmonic Oscillator

Abstract

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