Linearity, Symmetry, and Prediction in the Hydrogen Atom
(Sprache: Englisch)
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 linear model of quantum mechanics Method has wide applications in crystallography, atomic structure,...
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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 linear model of quantum mechanics Method has wide applications in crystallography, atomic structure, classification of manifolds with symmetry and other areas Engaging and vivid style Driven by numerous exercises and examples Systematic organization Separate solutions manual available
Klappentext zu „Linearity, Symmetry, and Prediction in the Hydrogen Atom “
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 linear model of quantum mechanics
Method has wide applications in crystallography, atomic structure, classification of manifolds with symmetry and other areas
Engaging and vivid style
Driven by numerous exercises and examples
Systematic organization
Separate solutions manual available
The predictive power of mathematics in quantum phenomena is one of the great intellectual successes of the 20th century. This textbook, 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.
The topics unfold systematically, introducing the reader first to an important example of a quantum system with symmetry, the single electron in a hydrogen atom. 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. Linearity, Symmetry, and Prediction in the Hydrogen Atomwill benefit students in mathematics, physics and chemistry, as well as a literate general readership.
A separate solutions manual is available to instructors.
The topics unfold systematically, introducing the reader first to an important example of a quantum system with symmetry, the single electron in a hydrogen atom. 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. Linearity, Symmetry, and Prediction in the Hydrogen Atomwill benefit students in mathematics, physics and chemistry, as well as a literate general readership.
A separate solutions manual is available to instructors.
Inhaltsverzeichnis zu „Linearity, Symmetry, and Prediction in the Hydrogen Atom “
- 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
- Represenatations 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
- A. Spherical Harmonics
- B. Proof of the Correspondence
- C. Suggested Paper Topics
- Bibliography
- Index
- References.
Autoren-Porträt von Stephanie Frank Singer
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.
Bibliographische Angaben
- Autor: Stephanie Frank Singer
- 2005, 398 Seiten, Maße: 16,4 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer, New York
- ISBN-10: 0387246371
- ISBN-13: 9780387246376
Sprache:
Englisch
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