University of Nice textbook on Quantum Physics by Michel Le Bellac translated by Patricia de Forcrand-Millard.
Published on 06/18/2019
Document details: 81 downloads.
In Quantum Mechanics operators must be hermitian and, in a direct product space, symmetric. These properties are saved by Lie algebra operators but not by those of quantum algebras. A possible correspondence between observables and quantum algebra operators is suggested by extending the definition of matrix elements of a physical observable, including the eventual projection on the appropriate symmetric space. This allows to build in the Lie space of representations one-parameter families of operators belonging to the enveloping Lie algebra that satisfy an approximate symmetry and have the properties required by physics.
Published on 09/23/2013
Document details: 307 downloads.
Physics of Quantum mechanics
Published on 03/11/2019
Document details: 75 downloads.
Quantum Theory encompasses our best understanding of how nature works: what will be the result of any experiment. We arbitrarily split the universe into �system� (wave function), an environment or measurement (Hamiltonian, or operator) and a measureable quantity (eigenvalue). There is no unique associated mathematics, but since all measurements on systems yield real numbers, we need mathematics which gives real eigenvalues. So it is a premise of quantum theory that any measurable quantity is associated with a Hermitian operator.
Published on 11/14/2013
Document details: 61 pages. 664 downloads.
The conceptual problems in quantum mechanics -- related to the collapse of the wave function, the particle-wave duality, the meaning of measurement -- arise from the need to ascribe particle character to the wave function. As will be shown, all these problems dissolve when working instead with quantum fields, which have both wave and particle character. Otherwise the predictions of quantum physics, including Bell's inequalities, coincide with those of the standard treatments. The transfer of the results of the quantum measurement to the classical realm is also discussed.
Published on 09/19/2013
Document details: 61 pages. 113 downloads.
Motivated by Feynman's 1983 paper on the simulation of physics by computers, we present a general approach to the description of quantum experiments which uses quantum bit registers to represent the spatio-temporal changes occurring in apparatus-systems during the course of such experiments. To illustrate our ideas, we discuss the Stern-Gerlach experiment, Wollaston prisms, beam splitters, Mach-Zender interferometers, von Neumann (PVM) tests, the more general POVM formalism, and a variety of modern quantum experiments, such as two-particle interferometry and the EPR scenario.
Published on 09/22/2013
Document details: 61 pages. 60 downloads.
Learning goals for 8.04 � boundary between classical and quantum physics � understand crucial experiments that paved way for development of quantum mechanics � understand & interiorize probability amplitude and interference concepts that are at the heart of QM � single-particle quantum mechanics for external degrees of freedom; Schr�odinger equation � internal degrees of freedom; e.g., spin: 8.05; many body quantum physics: 8.06 and beyond � some formal structure of QM (operators, expectation values, commutators, Dirac notation) further development: 8.05 � understand interface between mathematical structure (Schr�odinger equation as partial di_erential equation) and physical interpretation, measurement, uncertainty, correlations, and entanglement � study important QM systems: harmonic oscillator, hydrogen atom � At the end of this course you should be able to: - solve simple QM single-particle problems in one and three dimensions (scattering, tunneling, bound states) - give a physical interpretation of mathematical entities (operators, wavefunction, state representation in di_erent bases, Fourier transform, Heisenberg uncertainty relation) - appreciate & understand the all-importance of interference e_ect (addition of probability amplitudes) in QM � 8.04: only non-relativistic QM
Published on 11/13/2013
Document details: 4 pages. 353 downloads.
Published on 05/04/2012
Document details: 310 pages. 300 downloads.
Green's Functions in Quantum Physics
Published on 02/20/2019
Document details: 310 pages. 116 downloads.
In the past decade quantum algorithms have been found which outperform the best classical solutions known for certain classical problems as well as the best classical methods known for simulation of certain quantum systems. This suggests that they may also speed up the simulation of some classical systems. I describe one class of discrete quantum algorithms which do so--quantum lattice gas automata--and show how to implement them efficiently on standard quantum computers.
Published on 09/22/2013
Document details: 310 pages. 57 downloads.