Engineering

For Quantum Mechanics courses in departments of electrical engineering, materials science, and physics.

This book is designed to meet the changing quantum mechanics needs of general and applied physicists in such areas as solid state research, quantum electronics, materials science, etc. It recognizes that these needs go significantly beyond most elementary texts, and at the same time have become sufficiently distinct from the traditional advanced treatment of quantum mechanics.

• uses new and less abstract ways to present formal concepts—without sacrificing rigor.

  • justifies new concepts first by intuitive physical arguments, and then provides more rigor, after the meaning of the concepts is understood physically and qualitatively

• the expectation value concept is introduced early, and it forms the basis for much of what follows, from the operator formalism to the variational principle.

• perturbation theory is viewed as the backbone of practical quantum mechanics, and is developed extensively. The treatment of non- degenerate perturbation theory goes beyond the usual Rayleigh-Schroedinger formalism, and emphasizes the Brillouin-Wigner algorithmic formalism, that is no more difficult, but is much more powerful—and ideally suited for computer implementation.

• the importance of geometrical symmetries in quantum-mechanical problems is developed in depth, culminating in a Section “Group Theroy for Pedestrians,” that gives the reader a working knowledge of the power of group-theoretical arguments—without having to learn the full abstract apparatus.

• two chapters on time-dependent perturbations cover such topics as Fermi's Golden Rule, indirect transitions, and radiation processes. The treatment of the latter moves beyond the semi-classical approximation, to a stripped-down but honest quantized-field formulation, and from that to an in- depth understanding of spontaneous and stimulated emission. A highly- simplified treatment of photon correlations and the Bell Inequality is given.

 1. Wave-Particle Duality and Schroedinger Equation.


 2. Introduction to Bound States.


 3. Rotationally Invariant Potentials: Hydrogen Atom and Beyond.


 4. Wave Packets and Uncertainty Relations.


 5. Scattering by Simple Barriers.


 6. WKB Approximations.


 7. Expectation Values and Operators.


 8. Electrons in a Magnetic Field.


 9. Beyond Hermitian Operators.


10. Harmonic Oscillator: Full Operator Treatment.


11. Composite Systems.


12. Variational Principle.


13. Expansion Principle and Matrix Formulation.


14. Perturbation Theory, I: "Degenerate" Perturbation Theory.


15. Perturbation Theory, II: "Non-Degenerate" Perturbation Theory.


16. Symmetry.


17. Electrons in Periodic Crystal Potentials.


18. Rotational Invariance and Angular Momentum.


19. Time-Dependent Perturbation Theory.


20. Elements of Field Quantization.


21. Electron Spin.


22. Indistinguishable Particles: Fermions and Bosons.


Appendices: Dirac …d-Function. Poisson-Distributed Events. Spherical Harmonics. Hydrogen Radial Eigenfunctions. Fourier Integral. Construction of Two Group Character Tables. Selected General References. Fundamental Constants.


Index.

Quantum Mechanics  [OTHER TITLES OF INTEREST]   (Electrical and Computing Engineering)

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