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Transformation theory (quantum mechanics)
About: Transformation theory (quantum mechanics) is a research topic. Over the lifetime, 97 publications have been published within this topic receiving 7759 citations.
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01 Jan 1996
TL;DR: The Mathematical Foundations of Quantum Mechanics as discussed by the authors is a seminal work in theoretical physics that introduced the theory of Hermitean operators and Hilbert spaces and provided a mathematical framework for quantum mechanics.
Abstract: Mathematical Foundations of Quantum Mechanics was a revolutionary book that caused a sea change in theoretical physics. Here, John von Neumann, one of the leading mathematicians of the twentieth century, shows that great insights in quantum physics can be obtained by exploring the mathematical structure of quantum mechanics. He begins by presenting the theory of Hermitean operators and Hilbert spaces. These provide the framework for transformation theory, which von Neumann regards as the definitive form of quantum mechanics. Using this theory, he attacks with mathematical rigor some of the general problems of quantum theory, such as quantum statistical mechanics as well as measurement processes. Regarded as a tour de force at the time of publication, this book is still indispensable for those interested in the fundamental issues of quantum mechanics.
4,043 citations
TL;DR: It is shown that nonequilibrium may become a source of order and that irreversible processes may lead to a new type of dynamic states of matter called "dissipative structures" and the thermodynamic theory of such structures is outlined.
Abstract: Fundamental conceptual problems that arise from the macroscopic and microscopic aspects of the second law of thermodynamics are considered. It is shown that nonequilibrium may become a source of order and that irreversible processes may lead to a new type of dynamic states of matter called "dissipative structures." The thermodynamic theory of such structures is outlined. A microscopic definition of irreversible processes is given, and a transformation theory is developed that allows one to introduce nonunitary equations of motion that explicitly display irreversibility and approach to thermodynamic equilibrium. The work of the group at the University of Brussels in these fields is briefly reviewed. In this new development of theoretical chemistry and physics, it is likely that thermodynamic concepts will play an ever-increasing role.
864 citations
TL;DR: In this paper, a simple method using the techniques of transformation theory for the generation of the matrix elements of unusual potential functions for one-dimensional quantum-mechanical problems is described.
Abstract: A simple method using the techniques of transformation theory for the generation of the matrix elements of unusual potential functions for one‐dimensional quantum‐mechanical problems is described. It is applicable both to functions which exist as a set of points, for example, a curve or table, as well as to those in explicit form. Some representative calculations have been made for anharmonic oscillators.
555 citations
TL;DR: Matrix elements calculation for one dimensional quantum-mechanical problems using transformation theory using matrix elements was studied in this paper, where transformation theory was used to solve the problem of matrix elements calculation.
Abstract: Matrix elements calculation for one dimensional quantum-mechanical problems using transformation theory
383 citations
TL;DR: In this article, an innovative technique of integration within an ordered product (IWOP) of operators was proposed, which made the integration of non-commutative operators possible and further revealed the beauty and elegance of Dirac's symbolic method and transformation theory.
317 citations