Practical Quantum Mechanics: Modern Tools and Applications

Hardcover | November 25, 2015

byEfstratios Manousakis

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Quantum mechanics forms the foundation of all modern physics, including atomic, nuclear, and molecular physics, the physics of the elementary particles, condensed matter physics. Modern astrophysics also relies heavily on quantum mechanics. Quantum theory is needed to understand the basis fornew materials, new devices, the nature of light coming from stars, the laws which govern the atomic nucleus, and the physics of biological systems. As a result the subject of this book is a required course for most physics graduate students. While there are many books on the subject, this book targets specifically graduate students and it is written with modern advances in various fields in mind. Many examples treated in the various chapters as well as the emphasis of the presentation in the book are designed from the perspective ofsuch problems. For example, the book begins by putting the Schrodinger equation on a spatial discrete lattice and the continuum limit is also discussed, inspired by Hamiltonian lattice gauge theories. The latter and advances in quantum simulations motivated the inclusion of the path integralformulation. This formulation is applied to the imaginary-time evolution operator to project the exact ground state of the harmonic oscillator as is done in quantum simulations. As an example of how to take advantage of symmetry in quantum mechanics, one-dimensional periodic potentials arediscussed, inspired by condensed matter physics. Atoms and molecules are discussed within mean-field like treatment (Hartree-Fock) and how to go beyond it. Motivated by the recent intense activity in condensed matter and atomic physics to study the Hubbard model, the electron correlations in thehydrogen molecule are taken into account by solving the two-site Hubbard model analytically. Using the canonical Hamiltonian quantization of quantum electrodynamics, the photons emerge as the quanta of the normal modes, in the same way as the phonons emerge in the treatment of the normal modes ofthe coupled array of atoms. This is used later to treat the interaction of radiation with atomic matter.

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Quantum mechanics forms the foundation of all modern physics, including atomic, nuclear, and molecular physics, the physics of the elementary particles, condensed matter physics. Modern astrophysics also relies heavily on quantum mechanics. Quantum theory is needed to understand the basis fornew materials, new devices, the nature of li...

Efstratios Manousakis received his Ph. D. in Theoretical Physics, in 1985, from the University of Illinois at Urbana-Champaign. After a Post-Doctoral Research position at the Center for Theoretical Physics at the Massachusetts Institute of Technology (1985-1987) and at the Supercomputer Computational Research Institute (1987-88), he jo...
Format:HardcoverDimensions:352 pages, 9.69 × 6.73 × 0.1 inPublished:November 25, 2015Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198749341

ISBN - 13:9780198749349

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Table of Contents

1. Schrodinger equation on a lattice2. Dirac notation3. Back to Schrodinger equation on the lattice4. Operator-mechanics5. Time evolution and wave packets6. Simulaneaous observables7. Continuity equation and wavefunction properties8. Bond states in one-dimension9. Scattering in one dimension10. Periodic Potentials11. The harmonic oscillator12. WKB approximation13. Quantum mechanics and path integrals14. Applications of path integrals15. Angular momentum16. Bound states in spherically symmetric potentials17. The hydrogen-like atom18. Angular momentum and spherical symmetry19. Scattering in 3D20. Time independent perturbation expansion21. Applications of perturbation theory22. Time-dependent Hamiltonian23. Spin angular momentum24. Adding angular momenta25. Identical particles26. Elementary atomic physics27. Molecules28. The elasticity field29. Quantization of the free electromagnetic field30. Interaction of radiation with charged particles31. Elementary relativistic quantum mechanics

Editorial Reviews

"The book teaches students how to approach and solve the types of quantum mechanical problems they will encounter throughout their careers. It will serve as an excellent text for a graduate level course." --C. Stephen Hellberg, Naval Research Laboratory