Quantum Mechanics: Principles and Formalism - Brossura

McWeeny, R.

Brossura

ISBN 10: 048642829X ISBN 13: 9780486428291

Casa editrice: Dover Pubns, 2002

Riassunto

Concerned strictly with the principles and formalism of quantum mechanics, this graduate student-oriented volume develops the subject as a fundamental discipline. Opening chapters review the origins of Schrödinger's equations and the nature of the solutions in certain simple and well-known cases, advancing to the ideas associated with vector spaces. Having provided students with the appropriate mathematical language, the author proceeds to the formulation of the main principles of quantum mechanics and their immediate consequences. The book concludes with final generalizations in which alternative "languages" or representations are discussed — each with reference to its specific advantages and applications — and the Dirac transformation theory is developed and explained.

Su questo libro

Contenuti:

Preface Chapter 1. Physical Basis of Quantum Theory 1.1 Particles and waves 1.2 The Schrödinger equation for a particle 1.3 Probability density and probability current 1.4 The classical limit for motion of a wave packet Chapter 2. Some Simple Solutions of Schrödiner's Equation 2.1 The particle in a container 2.2 The harmonic oscillator 2.3 The hydrogen atom. Atomic units 2.4 The free particle 2.5 One-dimensional step potential with finite potential height Chapter 3. Mathematical Digression 3.1 Preliminaries. Operators and eigenvalue equations 3.2 Eigenfunction expansions 3.3 Generalization to many variables 3.4 Linear vector spaces. Basic ideas 3.5 Matrix representation of operators 3.6 Change of representation 3.7 Hermitian operators and eigenvalue equations in vector space 3.8 Composition of vector spaces. Product space Chapter 4. General Formulation of Quantum Mechanics 4.1 The postulates 4.2 The state vector and its time development 4.3 The expectation value postulate 4.4 Significance of the eigenvalue equation 4.5 The uncertainty principle 4.6 Time-development and the energy-time uncertainty principle 4.7 The completeness of eigenfunction sets 4.8 Properties of the operators 4.9 Electron spin Chapter 5. General Theory of Representations 5.1 Dirac notation. Discrete case 5.2 An example. The harmonic oscillator 5.3 Dirac notation. Continuous case 5.4 Transformation theory. The momentum representation 5.5 The Schrödinger equation in momentum space 5.6 Time-evolution. The Heisenberg representation 5.7 Representation of incompletely specified states Appendix 1. The Schrödinger Equation in Generalized Coordinates Appendix 2. Separtion of Partial Differential Equations Appendix 3 Series Solution of Second-order Differential Equations Appendix 4 Projection Operators and Normal Forms Index

Su questa edizione

• Editore: Dover Pubns
• Data di pubblicazione: 2002
• ISBN 10: 048642829X
• ISBN 13: 9780486428291
• Rilegatura: Copertina flessibile
• Numero di pagine: 168