This original and innovative textbook takes the unique perspective of introducing and solving problems in quantum mechanics using linear algebra methods, to equip readers with a deeper and more practical understanding of this fundamental pillar of contemporary physics. Extensive motivation for the properties of quantum mechanics, Hilbert space, and the Schrödinger equation is provided through analysis of the derivative, while standard topics like the harmonic oscillator, rotations, and the hydrogen atom are covered from within the context of operator methods. Advanced topics forming the basis of modern physics research are also included, such as the density matrix, entropy, and measures of entanglement. Written for an undergraduate audience, this book offers a unique and mathematically self-contained treatment of this hugely important topic. Students are guided gently through the text by the author's engaging writing style, with an extensive glossary provided for reference and numerous homework problems to expand and develop key concepts. Online resources for instructors include a fully worked solutions manual and lecture slides.
Author(s): Andrew J. Larkoski
Edition: 1
Publisher: Cambridge University Press
Year: 2022
Language: English
Pages: 398
1 - Introduction pp 1-4
2 - Linear Algebra pp 5-26
3 - Hilbert Space pp 27-57
4 - Axioms of Quantum Mechanics and their Consequences pp 58-88
5 - Quantum Mechanical Example: The Infinite Square Well pp 89-108
6 - Quantum Mechanical Example: The Harmonic Oscillator pp 109-133
7 - Quantum Mechanical Example: The Free Particle pp 134-169
8 - Rotations in Three Dimensions pp 170-200
9 - The Hydrogen Atom pp 201-240
10 - Approximation Techniques pp 241-267
11 - The Path Integral pp 268-298
12 - The Density Matrix pp 299-336
13 - Why Quantum Mechanics? pp 337-344
Appendices pp 345-355
A - Mathematics Review pp 345-350
B - Poisson Brackets in Classical Mechanics pp 351-353
C - Further Reading pp 354-355
Glossary pp 356-367
Bibliography pp 368-374
Index pp 375-380
