دانلود کتاب تسلط بر مکانیک کوانتومی

This book is the result of the author’s forty plus years of researching and teaching quantum mechanics. It is meant for students who have had some prior exposure to quantum mechanics and want to move to the next level. This book aims to lift those who are a little behind, and at the same time, give a new perspective for those who are more advanced. The book covers material for a two-semester or a three-quarter course. The assumed prerequisites include some classical mechanics and electrodynamics. As some prior exposure to quantum mechanics is also assumed, experimental indications are not treated here, and the most basic topics are reviewed only briefly. On the other hand, important concepts that probably have been discussed before cannot be left out without risk of breaking the logic of this presentation. The book tries to cover the basic topics from different, possibly more advanced, perspectives. The text starts with Mathematical Foundations, which provides a sound introduction to the required mathematics, like Hilbert spaces, Hermitian and unitary operators, invariant quantities, basis transformations, and functions of operators. The next chapter is about the Basics of Quantum Mechanics. Here the postulates are presented, together with the various pictures, the representation of operators, uncertainty relations and some consequences of continuous and discrete symmetries. A lot of physics can be explained by using the examples of One-Dimensional Problems. The general properties of the wave function are described in this chapter. The connection between bound-state and scattering quantities, together with timedependent aspects, are established by using the technique of analytic continuation. Also, harmonic oscillators and periodic potential models are treated in detail. The heavy industry of quantum mechanics starts with Angular Momentum. This chapter covers the quantization of angular momentum, orbital angular momentum, spin, rotation matrices, coupling schemes, rotation operators, spherical tensors and the Wigner-Eckart theorem. The next chapter is about Quantum Problems in Higher Dimensions. The covered topics include the usual harmonic-oscillator and Coulomb problems, charged particles in a magnetic field, and the consequences of the gauge transformation of the electromagnetic potentials, including the Aharonov-Bohm effect with the quantization of magnetic flux. In the chapter on Identical Particles in Quantum Mechanics, it is shown how the concept of indistinguishability of quantum particles leads to the symmetry of the wave function. In Approximation Methods for Time-Independent Problems, a wide range of methods are presented, including the Hellmann-Feynman theorem, the Rayleigh- Schrodinger and Brillouin-Wigner perturbation methods, variational methods, the semiclassical approximation method, and related applications. The Time-Dependent Quantum Mechanics starts with the time-dependent perturbation theory and applies it to constant and harmonic perturbations. Then sudden and adiabatic approximations with dynamical and geometric phases are presented, together with detailed analysis of two-state systems. In the chapter about Electromagnetic Radiation, the electromagnetic field is quantized, which leads to the photon concept and the vacuum expectation of the field. Then atoms in a radiation field are considered, together with transition amplitudes for emission and absorption, the selection rules, and the natural broadening of spectral lines. Finally, the black-body radiation formulae are re-derived and the Casimir effect is discussed. Scattering Theory is about exploring the Hamiltonian. Knowing a few bound states gives rather limited information about the physical system. To get the full picture, we need scattering information as well. The treatment of quantum scattering goes through asymptotic states and resolvent operators in order to derive the properties of the wave function from the asymptotic analysis of the integral equations. Then the phase shift, the Jost function, the time delay, and the Levinson theorem are introduced. The treatment of scattering theory cannot be complete without considering two additional topics: the Coulomb scattering and three-body problems using the Faddeev approach. There are intimate relations between the two main pillars of modern physics, relativity and quantum mechanics. Their unification in Relativistic Quantum Mechanics presented us with the discovery of antiparticles, the electron spin, its coupling to the electromagnetic field, and so on. In Appendix, some Fortran codes for solving simple bound and scattering state problems are presented. This book should prepare students to take more advanced classes in the direction of many-body physics, quantum field theory, quantum optics, nuclear and particle physics, condensed-matter physics, and similar disciplines. I am thankful to my friends and colleagues Benjamin P. Carter, Scott M. Keller, DerekWingard and Robert Woodhouse for critical reading of the manuscript and to Attila Csótó for his help in clarifying some items. While I was on sabbatical leave, colleagues Michael R. Peterson and Andreas Bill taught my class from this manuscript and provided feedback with pertinent suggestions. Special thanks is due to Sergey L. Yakovlev for his help and several constructive suggestions.