量子力学 英文
作者：（美）B.C.里德（Bruce Cameron Reed）著
出版时间：2018年版
内容简介
This text is directed at the needs of physics and chemistry students in smaller colleges and universities who are encountering their first serious course in quantum mechanics （QM）， typically at about the junior level. The curricula of such institutions often leaves room for only one semester of QM as opposed to the two or more that are com-mon at larger schools， so such students face Lhe task of trying to absorb in a short time boLh the underlying physics and mathematical formalism of quantum theory. My goal is to give students a sense of “where it all leads” before they encounter that full math-ematical formalism in， say， a senior-level or first graduate course by providing a treatment of the basic theories and results of wave mechanics that falls intermediate between sophomore-level “modern physics” texts and those typical of more advanced treatments.
Background preparation assumed here includes advanced calculus （partial differ-entiation and multiple integration）； some exposure to basic concepts of differential equations （particularly the series solution method）； vector calculus in Cartesian， spher-ical， and cylindrical coordinates； and the standard menu of physics courses： mechan-ics， electricity and magnetism， and modern physics. Some previous exposure to the historical context from which quantum mechanics developed is helpful but not strict-Iy necessary as these matters are reviewed briefly in Chapter 1.
I am firmly of the belief that it is only by working through the derivations of a number of classical problems and by doing numerous homework exercises can stu-dents come to develop a feeling for the conceptual content of quantum mechanics and the necessary analytic skills involved in actually applying it. Present-day physics rep-resents the cumulative knowledge of a chain of reasoning and experiment that stretch-es back over centuries， and it is important for students to have a sense of how we came to be where we are. Consequently， this book emphasizes the development of exact or approximate analytic solutions to Schrodinger's equation （SE）， that is， solutions that can be expressed in algebraic form. To this end， the layout of this book follows a fair-ly conventional ordering. Chapter I reviews some of the developments of early twen-tieth-century physics that indicated the need for a radical rethinking of fundamental physical laws on the atomic scale： Planck's quantum hypothesis， the Rutherford-Bohr atomic model， and de Broglie's matter-wave concept. Chapter 2 develops the SE， the fundamental “Iaw” of quantum mechanics. Chapter 3 explores applications of the SE to one-dimensional problems （potential wells and barriers）， working up to a treatment of alpha-decay as a barrier-penetration phenomenon. Chapter 4 forms a sort of inter-mission to introduce some of the mathematical formalisms of QM such as operators，expectation values， the uncertainty principle， Ehrenfest's theorem， the orthogonality theorem， the superposition principle， the virial theorem， and Dirac notation. Chapter 5 is devoted to an analysis of the important harmonic-oscillator potential. Extension of the SE to three dimensions appears in Chapter 6， along with a treatment of separation of variables and angular momentum operators for central potentials. These develop-ments set the stage for a fairly rigorous analysis of the Coulomb potential in Chapter 7. Chapter 8 deals with some more advanced aspects of angular momentum， and can be considered optional. Chapter 9 explores techniques for obtaining approximate ana-lytic solutions of the SE in situations where full analytic solutions are too difficult or impossible to achieve： the WKB method， perturbation theory， and the variational method. In view of the central role of computers in almost all contemporary research，Chapter 10 explores a simple algorithm for numerically integrating the SE with a Microsoft Excel spreadsheet. This chapter comes with an important caveat， however：no physicist， either beginning student or seasoned researcher， should ever let playingwith a computer become a substitute for first exploring a problem conceptually and analytically. The emphasis in this book is on the time-independent SE， but a taste of some results of considering time-dependence are taken up briefly in Chapter 11. A few particularly lengthy mathematical derivations oflimited physical content are gathered together in Appendix A. Answers to a number of the end-of-chapter problems appear in Appendix B. Appendices C and D list a number of useful integrals， mathematical identities， and physical constants.
