 | |
| Author | Ramamurti Shankar |
|---|---|
| Country | United States |
| Language | English |
| Subject | Quantum mechanics |
| Genre | Non-fiction |
| Published | March 2011 (2nd edition) |
| Publisher | Plenum Press |
| ISBN | 0306447908 |
Principles of Quantum Mechanics is a textbook by Ramamurti Shankar. [1] The book has been through two editions. It is used in many college courses around the world. [2] [3] [4]
Physics Bulletin said about the book, "No matter how gently one introduces students to the concept of Dirac’s bras and kets, many are turned off. Shankar attacks the problem head-on in the first chapter, and in a very informal style suggests that there is nothing to be frightened of". [5] American Scientist called it "An excellent text … The postulates of quantum mechanics and the mathematical underpinnings are discussed in a clear, succinct manner". [6]
The mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. This mathematical formalism uses mainly a part of functional analysis, especially Hilbert spaces, which are a kind of linear space. Such are distinguished from mathematical formalisms for physics theories developed prior to the early 1900s by the use of abstract mathematical structures, such as infinite-dimensional Hilbert spaces, and operators on these spaces. In brief, values of physical observables such as energy and momentum were no longer considered as values of functions on phase space, but as eigenvalues; more precisely as spectral values of linear operators in Hilbert space.
In physics, quantization is the systematic transition procedure from a classical understanding of physical phenomena to a newer understanding known as quantum mechanics. It is a procedure for constructing quantum mechanics from classical mechanics. A generalization involving infinite degrees of freedom is field quantization, as in the "quantization of the electromagnetic field", referring to photons as field "quanta". This procedure is basic to theories of atomic physics, chemistry, particle physics, nuclear physics, condensed matter physics, and quantum optics.
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science.
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic behavior of nature from the behavior of such ensembles.
The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics. The equation is named after Erwin Schrödinger, who postulated the equation in 1925 and published it in 1926, forming the basis for the work that resulted in his Nobel Prize in Physics in 1933.
In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middle step that breaks the problem into "solvable" and "perturbative" parts. In perturbation theory, the solution is expressed as a power series in a small parameter . The first term is the known solution to the solvable problem. Successive terms in the series at higher powers of usually become smaller. An approximate 'perturbation solution' is obtained by truncating the series, usually by keeping only the first two terms, the solution to the known problem and the 'first order' perturbation correction.
Mathematical physics refers to the development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines the field as "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories". An alternative definition would also include those mathematics that are inspired by physics.
The stationary-action principle – also known as the principle of least action – is a variational principle that, when applied to the action of a mechanical system, yields the equations of motion for that system. The principle states that the trajectories are stationary points of the system's action functional. The term "least action" is a historical misnomer since the principle has no minimality requirement: the value of the action functional need not be minimal on the trajectories.
Boris Yakovlevich Podolsky was a Russian-American physicist of Jewish descent, noted for his work with Albert Einstein and Nathan Rosen on entangled wave functions and the EPR paradox.
In theoretical physics, Euclidean quantum gravity is a version of quantum gravity. It seeks to use the Wick rotation to describe the force of gravity according to the principles of quantum mechanics.
Asım Orhan Barut was a Turkish-American theoretical physicist.
The ensemble interpretation of quantum mechanics considers the quantum state description to apply only to an ensemble of similarly prepared systems, rather than supposing that it exhaustively represents an individual physical system.
The history of quantum mechanics is a fundamental part of the history of modern physics. Quantum mechanics' history, as it interlaces with the history of quantum chemistry, began essentially with a number of different scientific discoveries: the 1838 discovery of cathode rays by Michael Faraday; the 1859–60 winter statement of the black-body radiation problem by Gustav Kirchhoff; the 1877 suggestion by Ludwig Boltzmann that the energy states of a physical system could be discrete; the discovery of the photoelectric effect by Heinrich Hertz in 1887; and the 1900 quantum hypothesis by Max Planck that any energy-radiating atomic system can theoretically be divided into a number of discrete "energy elements" ε such that each of these energy elements is proportional to the frequency ν with which each of them individually radiate energy, as defined by the following formula:
The Feynman checkerboard, or relativistic chessboard model, was Richard Feynman’s sum-over-paths formulation of the kernel for a free spin-½ particle moving in one spatial dimension. It provides a representation of solutions of the Dirac equation in (1+1)-dimensional spacetime as discrete sums.
Classical Mechanics is a textbook about that subject written by Herbert Goldstein, a professor at Columbia University. Intended for advanced undergraduate and beginning graduate students, it has been one of the standard references in its subject around the world since its first publication in 1950.
The Principles of Quantum Mechanics is an influential monograph on quantum mechanics written by Paul Dirac and first published by Oxford University Press in 1930. Dirac gives an account of quantum mechanics by "demonstrating how to construct a completely new theoretical framework from scratch"; "problems were tackled top-down, by working on the great principles, with the details left to look after themselves". It leaves classical physics behind after the first chapter, presenting the subject with a logical structure. Its 82 sections contain 785 equations with no diagrams.
Thermodynamics and an Introduction to Thermostatistics is a textbook written by Herbert Callen that explains the basics of classical thermodynamics and discusses advanced topics in both classical and quantum frameworks. It covers the subject in an abstract and rigorous manner and contains discussions of applications. The textbook contains three parts, each building upon the previous. The first edition was published in 1960 and a second followed in 1985.
Lectures on Theoretical Physics is a six-volume series of physics textbooks translated from Arnold Sommerfeld's classic German texts Vorlesungen über Theoretische Physik. The series includes the volumes Mechanics, Mechanics of Deformable Bodies, Electrodynamics, Optics, Thermodynamics and Statistical Mechanics, and Partial Differential Equations in Physics. Focusing on one subject each semester, the lectures formed a three-year cycle of courses that Sommerfeld repeatedly taught at the University of Munich for over thirty years. Sommerfeld's lectures were famous and he was held to be one of the greatest physics lecturers of his time.
Modern Quantum Mechanics, often called Sakurai or Sakurai and Napolitano, is a standard graduate-level quantum mechanics textbook written originally by J. J. Sakurai and edited by San Fu Tuan in 1985, with later editions coauthored by Jim Napolitano. Sakurai died in 1982 before he could finish the textbook and both the first edition of the book, published in 1985 by Benjamin Cummings, and the revised edition of 1994, published by Addison-Wesley, were edited and completed by Tuan posthumously. The book was updated by Napolitano and released two later editions. The second edition was initially published by Addison-Wesley in 2010 and rereleased as an eBook by Cambridge University Press, who released a third edition in 2020.
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