Linearity, Symmetry, and Prediction in the Hydrogen Atom

2005
ISBN: 978-1-4419-2035-5
Verlag: Springer

Buch, Englisch, 398 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 622 g

Reihe: Undergraduate Texts in Mathematics

This undergraduate textbook concentrates on how to make predictions about dimensions of the basic states of a quantum system from only two ingredients: the symmetry and the linear model of quantum mechanics. This method, known as representation theory or group theory, combines three core mathematical subjects, namely, linear algebra, analysis and abstract algebra and finds wide applications in crystallography, classification of manifolds with symmetry, atomic structure, and so on. The reader is first introduced to an important example of a quantum system with symmetry, the single electron in an hydrogen atom; and then the reader is given just enough mathematical tools to make predictions about the numbers of each kind of electronic orbital based solely on the physical spherical symmetry of the hydrogen atom. The final chapters address the related ideas of quantum spin, measurement and entanglement.

This user-friendly exposition, driven by numerous examples and exercises, requires a solid background in calculus and familiarity with either linear algebra or advanced quantum mechanics. This book will benefit students in mathematics, physics and chemistry, as well as a literate general readership.

A separate solutions manual is available to instructors.

Zielgruppe

Graduate

Autoren/Hrsg.

Singer, Stephanie Frank

Fachgebiete

• Naturwissenschaften Physik Quantenphysik Atom- und Molekülphysik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

Setting the Stage.- Linear Algebra over the Complex Numbers.- Complex Scalar Product Spaces (a.k.a. Hilbert Spaces).- Lie Groups and Lie Group Representations.- New Representations from Old.- Irreducible Representations and Invariant Integration.- Representations and the Hydrogen Atom.- The Algebra so(4) Symmetry of the Hydrogen Atom.- The Group SO(4) Symmetry of the Hydrogen Atom.- Projective Representations and Spin.- Independent Events and Tensor Products.

Über Autor(innen)

Stephanie Frank Singer received her Ph.D. in Mathematics from the Courant Institute in 1991. In 2002 she resigned her tenured professorship at Haverford College. Since then she has been writing and consulting independently. Her first book was Symmetry In Mechanics: A Gentle, Modern Introduction.