Linearity, symmetry, and prediction in the hydrogen atom
General Material Designation
[Book]
First Statement of Responsibility
/ Stephanie Frank Singer
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
New York
Name of Publisher, Distributor, etc.
: Springer,
Date of Publication, Distribution, etc.
, c2005.
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
xiv, 396 p. , ill.
SERIES
Series Title
(Undergraduate texts in mathematics)
NOTES PERTAINING TO PUBLICATION, DISTRIBUTION, ETC.
Text of Note
Electronic
INTERNAL BIBLIOGRAPHIES/INDEXES NOTE
Text of Note
Includes bibliographical references (p. [379]-384) and index.
CONTENTS NOTE
Text of Note
"The predictive power of mathematics in quantum phenomena is one of the great intellectual successes of the 20th century. This textbook, which is aimed at undergraduate or graduate level students (depending on the college or university) concentrates on how to make predictions about the numbers of each kind of basic state of a quantum system from only two ingredients: the symmetry and the linear model of quantum mechanics. This method, involving the mathematical area of representation theory or group theory, combines three core mathematical subjects, namely, linear algebra, analysis and abstract algebra. Wide applications of this method occur in crystallography, atomic structure, classification of manifolds with symmetry, and other areas." "This exposition, driven by numerous examples and exercises, requires a solid background in calculus and familiarity with either linear algebra or advanced quantum mechanics. Linearity, Symmetry, and Prediction in the Hydrogen Atom will benefit students in mathematics, physics and chemistry, as well as a literate general readership. A separate solutions manual is available to instructors."--BOOK JACKET.
Text of Note
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.