Kooperativer Bibliotheksverbund

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Format: 1 online resource (various pagings) : , illustrations (some color).

ISBN: 0-7503-1206-8 , 0-7503-1208-4

Series Statement: [IOP release 2]

Content: Quantum mechanics is one of the most brilliant and exciting theories of the 20th century. It has not only explained a wide range of phenomena but has brought revolutionary changes in the conceptual foundations of physics and continues to shape the modern world. As quantum mechanics involves the introduction of a new conceptual framework, the new ideas are explicitly mentioned and explained in detail in this book, and wherever possible, the various aspects of original thinking of eminent physicists are reflected. The emphasis is on helping students comprehend the significance of the underlying principles and understand the ways the new concepts were introduced. Including many worked examples and problems, this book will be an invaluable resource for students in physics, chemistry and electrical engineering needing a clear and rigorous introduction to quantum mechanics.

Note: "Version: 20151201"--Title page verso. , Preface -- Author biography -- 1. The failure of classical physics and the advent of quantum mechanics -- 1.1. A challenge for classical physics -- 1.2. The photoelectric effect -- 1.3. The Compton effect -- 1.4. Heisenberg's uncertainty principle -- 1.5. The correspondence principle -- 1.6. The Schrödinger wave equation -- 1.7. Constraints on solutions -- 1.8. Eigenfunctions and eigenvalues -- 1.9. The principle of superposition -- 1.10. Complementarity -- 1.11. Schrödinger's amplitude equation -- 1.12. The orthonormal set of functions -- 1.13. The equation of continuity -- 1.14. Complete sets of functions -- 1.15. The quantum theory of measurement -- 1.16. Observables and expectation values -- 1.17. Phases and relative phases -- 1.18. Postulates of quantum mechanics -- 1.19. The Schrödinger wave equation under space reflection, space inversion and time reversal -- 1.20. Concluding remarks , 2. A particle in a one-dimensional box -- 2.1. Introduction -- 2.2. The solution of Schrödinger's amplitude equation -- 2.3. Zero-point energy -- 2.4. The normalisation constant -- 2.5. The parity of eigenfunctions , 3. Free particles -- 3.1. Introduction -- 3.2. Free particles -- 3.3. Normalisation of stationary wave solutions -- 3.4. Normalisation of progressive wave solutions -- 3.5. Dirac's delta function -- 3.6. Continuous distribution of eigenvalues and Dirac's delta function -- 3.7. Eigenfunctions and eigenvalues of the position operator -- 3.8. Eigenfunctions and eigenvalues of the momentum operator -- 3.9. Normalisation of a free particle eigenfunction using a delta function , 4. Linear harmonic oscillator -- 4.1. Classical theory -- 4.2. Quantum theory -- 4.3. The asymptotic solution -- 4.4. The general solution -- 4.5. A physically acceptable solution -- 4.6. Energy eigenvalues -- 4.7. Hermite polynomials -- 4.8. The normalisation process -- 4.9. Probability distributions -- 4.10. The importance of the harmonic oscillator -- 4.11. Parity , 5. The role of Hermitian operators -- 5.1. Linear operators -- 5.2. Hermitian operators -- 5.3. The closure relation -- 5.4. Constants of motion -- 5.5. The classical limit of quantum mechanics : the Ehrenfest theorem -- 5.6. The virial theorem -- 5.7. Heisenberg's uncertainty principle -- 5.8. The parity operator -- 5.9. Antilinear operators -- 5.10. Antiunitary operators , 6. Potentials with finite discontinuities -- 6.1. Potential steps -- 6.2. The potential barrier -- 6.3. [alpha]-particle decay -- 6.4. The square-well potential , 7. Spherically symmetric potentials -- 7.1. Introduction -- 7.2. Spherically symmetric potentials -- 7.3. Separation of variables -- 7.4. Solution of the differential equation for F([phi]) -- 7.5. Solution of the differential equation for P([theta]) -- 7.6. Legendre polynomials and associated Legendre functions -- 7.7. Spherical harmonics -- 7.8. Hydrogen and hydrogenic atoms -- 7.9. The solution of the radial equation -- 7.10. Physically acceptable solutions for the radial equation and discrete energy values -- 7.11. The parity of a particle in a spherically symmetric potential -- 7.12. Comparison of the spectral series of hydrogen atom with experiments -- 7.13. The radial wave function -- 7.14. The spectroscopic notation -- 7.15. The normalised solution for the hydrogenic atom -- 7.16. Stationary states , 8. Matrix mechanics -- 8.1. Matrix representation of an operator -- 8.2. Change of basis and unitary transformation -- 8.3. Coordinate and momentum representations -- 8.4. Continuous distribution of eigenvalues , 9. Angular momentum -- 9.1. Angular momentum operator -- 9.2. Commutators of various components of L -- 9.3. Commutator of L2 and Lz -- 9.4. Components of the orbital angular momentum operator in spherical polar coordinates -- 9.5. L2 in spherical polar coordinates -- 9.6. Eigenfunctions and eigenvalues of Lz -- 9.7. Eigenvalues of Lz and L2 corresponding to their simultaneous eigenfunctions and ladder operators -- 9.8. Normal Zeeman effect -- 9.9. General theory of angular momentum -- 9.10. Characteristics of ladder operators -- 9.11. Electron spin -- 9.12. Matrix representations of Sx, Sy, Sz -- 9.13. Eigenvectors of Sz -- 9.14. The wave function for the electron -- 9.15. Spins of elementary particles -- 9.16. The average value of spin -- 9.17. Spin and statistics -- 9.18. Addition of angular momenta -- 9.19. Clebsch-Gordan coefficients , 10. Perturbation theory -- 10.1. Introduction -- 10.2. Time-independent perturbation theory for nondegenerate states -- 10.3. First-order correction to energy -- 10.4. The anomalous Zeeman effect -- 10.5. The first-order correction to the eigenfunction -- 10.6. Second-order non-degenerate perturbation -- 10.7. The second-order correction to energy -- 10.8. The second-order correction to the eigenfunction -- 10.9. First-order perturbation : energy correction in a two-fold degenerate case -- 10.10. The application of perturbation theory to the Stark effect -- 10.11. Time-dependent perturbation theory -- 10.12. Harmonic perturbation -- 10.13. Fermi's golden rule , 11. Theory of elastic scattering -- 11.1. Introduction -- 11.2. Centre-of-mass and laboratory frames of reference -- 11.3. The effect of collision on the velocity of the centre-of-mass in the laboratory frame -- 11.4. Relation between scattering angles in the laboratory and centre-of-mass frames -- 11.5. Relation between differential cross sections in the laboratory and centre-of-mass frames -- 11.6. Scattering by a stationary target -- 11.7. Relation between the scattering amplitude and differential cross section -- 11.8. Computation of the scattering amplitude -- 11.9. The Born approximation -- 11.10. Scattering of high energy electrons by a screened Coulomb potential -- 11.11. Partial wave analysis -- 11.12. The incident particle wave in terms of partial waves -- 11.13. Phase shift and scattering -- 11.14. A general solution in terms of partial waves -- 11.15. Optical theorem -- 11.16. Scattering by a hard sphere -- 11.17. Scattering from a potential square well -- 11.18. s-wave scattering for a square-well potential -- 11.19. Resonance scattering -- 11.20. Zero-energy scattering and the scattering length -- 11.21. Identical particles , 12. Dirac's formalism -- 12.1. Introduction -- 12.2. Unitary operators -- 12.3. Unitary transformation -- 12.4. A particular unitary operator -- 12.5 Representations and change of basis -- 12.6. A one-dimensional oscillator -- 12.7. The relation between state vectors and wave functions -- 12.8. A free particle. , Also available in print. , Mode of access: World Wide Web. , System requirements: Adobe Acrobat Reader.

Additional Edition: ISBN 0-7503-1207-6

Language: English

DOI: 10.1088/978-0-7503-1206-6