Elementary Quantum Mechanics

With Problems And Solutions

Stephen Wiggins (University Of Bristol, Uk & United States Naval Academy, Usa)

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Hardback

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English

World Scientific Publishing Co Pte Ltd
24 March 2025

Quantum physics (quantum mechanics & quantum field theory); Applied physics

Summary
Details

The impact of quantum mechanics

on our day-to-day life is growing at an exponential rate, of which most people are unaware. For example, the toaster is a prime example of a quantum mechanical device. While quantum mechanics arose as a subject in physics, quantum mechanical thinking has had, and continues to have, a broad impact on mathematics. For example, operator theory as we know it today would not exist without von Neumann's effort to put quantum mechanics on a solid mathematical foundation.

This book is defined for undergraduate students of mathematics to obtain an introduction to quantum mechanical ideas, and the associated mathematics, without requiring an extensive background in physics.

This book is focused around the following topics. 1) The Mathematical Structure of Quantum Mechanics. We develop the main mathematical structure of quantum theory

in the setting of the accepted postulates of quantum mechanics. Dirac's bra-ket notation for the required linear algebra aspects will be utilized, as well as the mathematical and physical implications arising from the mathematical aspects of self-adjoint linear operators, with emphasis on the finite dimensional setting. 2) Dynamics of a Quantum Particle. We introduce the Schrodinger equation and discuss its physical meaning and mathematical structure.

The required partial differential equations

theory is elementary, and will be developed from scratch. 3) Measurement, Time Evolution, Uncertainty, and the Harmonic Oscillator. This builds on the previously developed mathematics and culminates with a detailed discussion of the quantum mechanical workhorse example — the harmonic oscillator. 4) Quantum Mechanics of Angular Momentum.

Most of the book is developed in the context of the (relatively) simple one dimensional quantum systems. This topic goes into three dimensions and illustrates how very interesting mathematics can yield novel physical explanations that are unobtainable with classical methods. 5) The Postulates of Quantum Mechanics, Measurement, Composite Systems, Tensor Products, and Entanglement. This is the area that most students have heard of — quantum entanglement, 'action-at-a- distance' and Bell's inequality. The mathematics will be at an elementary level (except possibly for tensor products, which are sadly neglected many linear algebra courses today, but which are literally exploding in a variety of current applications).

By: Stephen Wiggins (University Of Bristol Uk & United States Naval Academy Usa)
Imprint: World Scientific Publishing Co Pte Ltd
Country of Publication: Singapore
ISBN: 9789819801855
ISBN 10: 9819801850
Pages: 268
Publication Date: 24 March 2025
Audience: College/higher education , Professional and scholarly , A / AS level , Undergraduate
Format: Hardback
Publisher's Status: Active