21. Quantum Mechanics - Wikipedia, The Free Encyclopedia quantum mechanics, also referred to as quantum physics, is a physical theory that describes the behavior of word for "quantity", hence the name "quantum mechanics.") The size of the http://www.wikipedia.org/wiki/Quantum_mechanics

Main Page Recent changes Edit this page Page history ... Printable version Not logged in Log in Help Other languages: Dansk Deutsch Galego Interlingua ... Svenska Quantum mechanics From Wikipedia, the free encyclopedia. Quantum mechanics , also referred to as quantum physics , is a physical theory that describes the behavior of matter at short length scales. The quantum theory provides a quantitative explanation for three types of phenomena that classical mechanics and classical electrodynamics cannot account for: Some observable physical quantities, such as the total energy of a blackbody , take on discrete rather than continuous values. This phenomenon is called quantization , and the smallest possible intervals between the discrete values are called quanta (singular: quantum , from the Latin word for "quantity", hence the name "quantum mechanics.") The size of the quanta typically varies from system to system. Under certain experimental conditions, microscopic objects like atoms or electrons exhibit wave-like behavior, such as interference . Under other conditions, the same species of objects exhibit particle-like behavior ("particle" meaning an object that can be localized to a particular region of

22. Measurement In Quantum Mechanics FAQ: Schrödinger's Cat English translation John D. Trimmer, Proceedings of the American Philosophical Society, 124, 32338 (1980), Reprinted in Quantum Theory and Measurement, p 152 http://www.mtnmath.com/faq/meas-qm-3.html

Previous Next Table of Contents Paul Budnik paul@mtnmath.com . A brief paragraph in this essay described the cat paradox. One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following diabolical device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small that perhaps in the course of one hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The first atomic decay would have poisoned it. The Psi function for the entire system would express this by having in it the living and the dead cat (pardon the expression) mixed or smeared out in equal parts. It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a ``blurred model'' for representing reality. In itself it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.

23. Philosophical Foundations Of Physics Positivist view of Physics, which had influenced the Copenhagen Interpretation of the quantum mechanics (CI). http://www.marxists.org/reference/subject/philosophy/works/ge/carnap.htm

Rudolph Carnap (1966) Philosophical Foundations of Physics Chapter 23: Theories and Nonobservables Source Philosophical Foundations of Physics (1966) publ. Basic Books Inc. Chapters 23 to 26 reproduced here. ONE OF THE most important distinctions between two types of laws in science is the distinction between what may be called (there is no generally accepted terminology for them) empirical laws and theoretical laws. Empirical laws are laws that can be confirmed directly by empirical observations. The term "observable" is often used for any phenomenon that can be directly observed, so it can be said that empirical laws are laws about observable. A philosopher might object that the intensity of an electric current is not really observed. Only a pointer position was observed. An ammeter was attached to the circuit and it was noted that the pointer pointed to a mark labelled 5.3. Certainly the current's intensity was not observed. It was inferred from what was observed. The physicist would reply that this was true enough, but the inference was not very complicated. The procedure of measurement is so simple, so well established, that it could not be doubted that the ammeter would give an accurate measurement of current intensity. Therefore, it is included among what are called observables. Empirical laws, in my terminology, are laws containing terms either directly observable by the senses or measurable by relatively simple techniques. Sometimes such laws are called empirical generalisations, as a reminder that they have been obtained by generalising results found by observations and measurements. They include not only simple qualitative laws (such as, "All ravens are black") but also quantitative laws that arise from simple measurements. The laws relating pressure, volume, and temperature of gases are of this type. Ohm's law, connecting the electric potential difference, resistance, and intensity of current, is another familiar example. The scientist makes repeated measurements, finds certain regularities, and expresses them in a law. These are the empirical laws. As indicated in earlier chapters, they are used for explaining observed facts and for predicting future observable events.

24. Quantum Mechanics -- From Eric Weisstein's World Of Physics quantum mechanics. General quantum mechanics. quantum mechanics. quantum mechanics is the description of world becomes important. quantum mechanics represented a fundamental break with http://www.treasure-troves.com/physics/QuantumMechanics.html

Modern Physics Quantum Physics Quantum Mechanics General Quantum Mechanics Quantum Mechanics Quantum mechanics is the description of motion and interaction of particles at the small scales where the discrete nature of the physical world becomes important. Quantum mechanics represented a fundamental break with classical physics , in which energies and angular momenta were regarded as continuous quantities that could change by arbitrary amounts. The first break with classical physics was performed by Planck who, in order to explain the observed spectrum of a blackbody, was forced to postulate that the oscillators in a blackbody could attain only certain quantized energies. Niels Bohr had a large influence on the development of quantum mechanics through his so-called " Copenhagen Interpretation ," a philosophical construct which was formulated to provide a fundamental framework for understanding the implicit assumptions, limitations, and applicability of the theory of quantum mechanics. Einstein subsequently postulated that electromagnetic radiation could exist only in discrete units, called

25. Quantum Mechanics - Wikipedia, The Free Encyclopedia quantum mechanics. quantum mechanics, also referred to as quantum physics, is a physical theory that describes the behavior of matter at short length scales. http://en.wikipedia.org/wiki/Quantum_mechanics

Main Page Recent changes Edit this page Page history ... Printable version Not logged in Log in Help Other languages: Dansk Deutsch Galego Interlingua ... Svenska Quantum mechanics From Wikipedia, the free encyclopedia. Quantum mechanics , also referred to as quantum physics , is a physical theory that describes the behavior of matter at short length scales. The quantum theory provides a quantitative explanation for three types of phenomena that classical mechanics and classical electrodynamics cannot account for: Some observable physical quantities, such as the total energy of a blackbody , take on discrete rather than continuous values. This phenomenon is called quantization , and the smallest possible intervals between the discrete values are called quanta (singular: quantum , from the Latin word for "quantity", hence the name "quantum mechanics.") The size of the quanta typically varies from system to system. Under certain experimental conditions, microscopic objects like atoms or electrons exhibit wave-like behavior, such as interference . Under other conditions, the same species of objects exhibit particle-like behavior ("particle" meaning an object that can be localized to a particular region of

26. Quantum Mechanics quantum mechanics is a mathematical theory that can describe the behavior of objects that are roughly 10,000,000,000 times smaller than a typical human being. http://rugth30.phys.rug.nl/quantummechanics/

help Preface Quantum mechanics is a mathematical theory that can describe the behavior of objects that are roughly 10,000,000,000 times smaller than a typical human being. Quantum particles move from one point to another as if they are waves. However, at a detector they always appear as discrete lumps of matter. There is no counterpart to this behavior in the world that we perceive with our own senses. One cannot rely on every-day experience to form some kind of "intuition" of how these objects move. The intuition or "understanding" formed by the study of basic elements of quantum mechanics is essential to grasp the behavior of more complicated quantum systems. The approach adopted in all textbooks on quantum mechanics is that the mathematical solution of model problems brings insight in the physics of quantum phenomena. The mathematical prerequisites to work through these model problems are considerable. Moreover, only a few of them can actually be solved analytically. Furthermore, the mathematical structure of the solution is often complicated and presents an additional obstacle for building intuition. This presentation introduces the basic concepts and fundamental phenomena of quantum physics through a combination of computer simulation and animation. The primary tool for presenting the simulation results is computer animation. Watching a quantum system evolve in time is a very effective method to get acquainted with the basic features and peculiarities of quantum mechanics. The images used to produce the computer animated movies shown in this presentation are not created by hand but are obtained by visualization of the simulation data. The process of generating the simulation data for the movies requires the use of computers that are far more powerful than Pentium III based PC 's. Most of the simulations require the use of a supercomputer. Consequently, within this presentation, it is not possible to change the model parameters and repeat a simulation in real time.

27. Homepage Of Doron Cohen BenGurion University. Research interests quantum mechanics, Quantum chaos, Theory of driven mesoscopic (nano) systems, Quantum irreversibility, Dissipation and dephasing. Publications. http://www.bgu.ac.il/~dcohen/

Doron Cohen PhD, Technion, Israel Institute of Technology, Haifa, Israel. RAFAEL,SCD,IAF,MOD The Weizmann Institute of Science, Rehovot, Israel. Harvard University, Cambridge, MA, USA. Ben-Gurion University, Beer-Sheva, Israel. more info BGU now article ... Scientific Calculator and Hebrew to Unicode converter Email: dcohen@bgu.ac.il Current Research Interest: Chaos and quantum mechanics ("Quantum Chaos"). Random Matrix Theory and Semiclassics. Theory of driven mesoscopic (nano) systems. Adiabatic transport and quantum pumping. Quantum irreversibility, dissipation and dephasing. Relation to quantum computing. Application to quantal Brownian Motion. My main line of study concerns driven systems that are described by time-dependent Hamiltonian H(Q,P;x(t)). Such systems absorb energy. This irreversible effect is known as dissipation. One aim of my studies is to develop a general theory for this energy absorption. The ohmic nature of dissipation and the associated fluctuation-dissipation relation are studied within the framework of quantum mechanics. It turns out that there are three regimes in the theory of energy absorption: The adiabatic regime; The linear-response (Kubo) regime; And the non-perturbative regime. The mesoscopic Drude formula for electrical conductance, and the wall formula for nuclear friction, can be regarded as special cases of the general formulation of the dissipation problem. The research plan involves numerical studies. Of particular interest are studies of so-called billiard systems. An important issue is to understand the clash between random matrix theory and semiclassical methods. [

28. Mark's Quantum Mechanics Applets Mark s quantum mechanics Applets. by Mark Sutherland. This is a collection of Java applets illustrating quantum mechanical processes. http://www.adnc.com/~topquark/quantum/quantumapplets.html

Mark's Quantum Mechanics Applets by Mark Sutherland This is a collection of Java applets illustrating quantum mechanical processes. The samples posted here are somewhat restricted in their functionality, but are still very useful for learning or teaching the concepts involved. Fully functional versions are available from the author. Hydrogen atom 2d slice Hydrogen atom in 3d Heisenberg's Uncertainty Principle Scattering from a 1-D square well ... The infinitely-deep square well

29. The Theory Of Positivist Mechanics - Abstract And Section 1: Introduction This theory proposed a framework by which the fundamental principles of quantum mechanics may be derived from classical (general relativistic) principles, thus providing a unification of GR and QM. http://www.geocities.com/straycat_md/TOPM.html

The Theory of Positivist Mechanics A Classical Solution to the Measurement Problem of Quantum Mechanics W. David Strayhorn, IV, Ph.D. (Cell Biology) Nashville, Tennessee January 2004 update: I have recently come up with a novel formulation of QM. You can access it my going to my briefcase , opening the papers folder, and downloading the MS Word document entitled Path Integrals and the MWI. Or you can see it online at: Path Integrals and the MWI (although some of the figures may not have transferred to html very nicely). The advantage of this formulation is that it is understandable; the "weirdness" is gone! In particular, there is a return to completely classical notions of probability. All of the usual conceptual difficulties associated with interference ("imaginary probabilities"? "negative probabilities"?) have vanished. And yet, it is 100% consistent with quantum theory. How can that possibly be? Read my paper! It seems to me that my formulation has matured to the level that it should be published. But before I go off and submit it, I would like to get some feedback. I would welcome any comments, which you can send to my yahoo! email address, or post in my yahoo! group, QM_from_GR. This is the abstract from "Path Integrals and the MWI:" In this essay I investigate the relationship between the Everett "relative state" formulation, also known as the multiple worlds interpretation (MWI), and Feynman’s path integral approach. To represent each of the "all possible paths" as unique entities within the MWI, I found it necessary to modify Everett’s original formulation slightly. This modification involves the addition of two separate principles: one that I justify by an appeal to its aesthetics, and one that is inspired by Hamilton’s least action principle. Despite these modifications, I argue that the resulting schema (1) makes the same predictions as quantum mechanics and (2) is easier to interpret than either the MWI or the path integral formulation alone. In particular, there is a return to purely classical notions of probability.

30. Quantum Mechanics A WebBased quantum mechanics Course. with In-Class Tutorials . Physics 521, quantum mechanics I, Fall 2000. The University of Tennessee http://electron6.phys.utk.edu/qm1/

A Web-Based Quantum Mechanics Course with In-Class Tutorials . Physics 521, Quantum Mechanics I, Fall 2000 The University of Tennessee, Department of Physics and Astronomy Marianne Breinig The University of Tennessee Department of Physics and Astronomy Note: This Website contains interactive elements which must be viewed with Internet Explorer 4 or higher.

31. Quantum Mechanics A WebBased quantum mechanics Course. with In-Class Tutorials . Physics 522, quantum mechanics II, Spring 2001. The University of http://electron6.phys.utk.edu/qm2/

A Web-Based Quantum Mechanics Course with In-Class Tutorials . Physics 522, Quantum Mechanics II, Spring 2001 The University of Tennessee, Department of Physics and Astronomy Marianne Breinig The University of Tennessee Department of Physics and Astronomy Note: This Website contains interactive elements which must be viewed with Internet Explorer 4 or higher.

32. 2. Some Basic Ideas About Quantum Mechanics University of Exeter 2. Some Basic Ideas about quantum mechanics. Modern physics is dominated by the concepts of quantum mechanics. http://newton.ex.ac.uk/research/semiconductors/theory/people/jenkins/mbody/mbody

2. Some Basic Ideas about Quantum Mechanics Modern physics is dominated by the concepts of Quantum Mechanics. This page aims to give a brief introduction to some of these ideas. Until the closing decades of the last century the physical world, as studied by experiment, could be explained according to the principles of classical (or Newtonian) mechanics: the physics of everyday life. By the turn of the century, however, the cracks were beginning to show and the disciplines of Relativity and Quantum Mechanics were developed to account for them. Relativity came first, and described the physics of very massive and very fast objects, then came Quantum Mechanics in the 1920's to describe the physics of very small objects. Neither of these theories provide an easy intuitive picture of the world, since they contradict the predictions of familiar Newtonian Mechanics in the regimes for which they were developed. Nevertheless, both schemes reproduce the Newtonian results when applied to the everyday world. In seeking to understand the physics of semiconductors at an atomic level we must start from a Quantum Mechanical viewpoint, since the entities with which we will be dealing (electrons, atoms, etc) are so very small....

33. PhysicsWeb - A Quantum Leap For Cosmology A theory that unites quantum mechanics and general relativity claims that there was no first moment in time, but it still agrees with the predictions of classical cosmology. http://physicsweb.org/article/world/14/11/3

Advanced site search physics world January February March April May June July August September October November December Latest issue Subscribe to Physics World Media Information ... Editorial Staff quick search Search Physics World Previous Physics World November 2001 Next A quantum leap for cosmology Physics in Action: November 2001 A theory that unites quantum mechanics and general relativity claims that there was no first moment in time, but it still agrees with the predictions of classical cosmology. It's in the stars One of the most challenging problems in modern physics is the application of quantum theory to the universe as a whole. Progress in this area has been plagued by two types of problem: conceptual and technical. The conceptual problems arise from the old difficulties of interpreting quantum theory. The standard interpretations require that the measuring instruments and observers are outside the quantum system described by the wavefunction. In the late 1950s, however, Hugh Everett proposed an interpretation of quantum theory that might apply to systems that include the observers and measuring instruments, but the adequacy of such interpretations has remained controversial to this day. The technical problems are no less severe or fundamental. Ever since the pioneering work of Bryce DeWitt, Charles Misner and others in the 1960s, quantum cosmology has basically been studied by applying quantum theory to simple models of the universe. These models typically assume that the universe is completely homogeneous. As a result they only have a few degrees of freedom - the radius of the universe and the value of one or more matter fields. One then makes a quantum-cosmological model by quantizing these simple descriptions of the universe.

34. Homepage Of Visual Quantum Mechanics Translate this page Presents a book that tries to explain the theroy behind quantum mechanics. This web site has information http://www.kfunigraz.ac.at/imawww/vqm/

35. Visual Quantum Mechanics - Sample Movies You need QuickTime to view these movies. Samples from Visual quantum mechanics. Samples from Advanced Visual quantum mechanics. http://www.kfunigraz.ac.at/imawww/vqm/pages/samples.html

36. Mark's Quantum Mechanics Applets A collection of sample Java applets which demonstrate various aspects of quantum mechanics, including the Hydrogen atom and Heisenberg's Uncertainty Principle. http://www3.adnc.com/~topquark/quantum/quantumapplets.html

Mark's Quantum Mechanics Applets by Mark Sutherland This is a collection of Java applets illustrating quantum mechanical processes. The samples posted here are somewhat restricted in their functionality, but are still very useful for learning or teaching the concepts involved. Fully functional versions are available from the author. Hydrogen atom 2d slice Hydrogen atom in 3d Heisenberg's Uncertainty Principle Scattering from a 1-D square well ... The infinitely-deep square well

37. Time Development Of Quantum Mechanical Systems Time development of quantum mechanical systems. Welcome to the world of quantum mechanics! Change to Hungarian language This document http://www.phy.bme.hu/education/schrd/

Time development of quantum mechanical systems Welcome to the world of quantum mechanics! Change to Hungarian language This document presents the results of the solution of the time dependent Schrodinger equation for one-, two-, and three dimensional one particle systems. Simulation results for different V(r) potentials are displayed as images and animation. The program to calculate the images is also available. See also our mailing list devoted to physics education programs! Introduction Influence of the wave packet shape to its time development Two dimensional (2D) one particle simulations Three dimensional (3D) one particle simulations NEW! Download the programs Physics education programs mailing list (If you want to receive notifications about the new uploads to this server subscribe now!) Address: Institute of Physics Technical University of Budapest H-1111 Budafoki ut. 8. Budapest, Hungary Europe Tel: (+36-1)463-4107, Fax: 463-3999 Last updated: May 2, 2001 mark@sunserv.kfki.hu

38. PDEase2D 3.0 Main Page Solves partial differential equations numerically by finite element analysis for use in such problems as heat transfer, reaction diffusion, solid and fluid mechanics, electromagnetics, groundwater flow, and quantum mechanics. http://www.scientek.com/macsyma/pdmain.htm

Finite Elements with No Mesh, No Fuss PDEase2D gives you a new way to solve partial differential equations (PDEs) numerically by finite element analysis. Flexible PDEase solves a very wide range of nonlinear problems in heat transfer, solid mechanics, fluid mechanics, groundwater flow, electromagnetics, chemical reaction diffusion, and quantum mechanics. It simplifies finite element analysis with automatic gridding, automated error analysis, flexible solution methods, and a simple input language. PDEase2D solves static, dynamic, and eigenvalue problems in two space dimensions, including PDEs of mixed elliptic, parabolic and hyperbolic type. Friendly PDEase has remarkably simple input. You merely specify the PDEs and variables, define the terms and material properties that occur in the equations, and specify the boundary shapes and conditions. PDEase2D includes 140 sample problems in mechanical, electrical and mechanical engineering Automated PDEase defines its own element grid, performs error analyses, and refines the grid as needed until error criteria are met. It solves nonlinear equations by iterative methods, adaptively selects time step size in dynamic problems, and draws plots using the Macsyma Front End (its own plots and Macsyma graphics). While users can intervene in these decisions, the software takes great care to usually make good decisions without user guidance. For particularly complicated equations or for curvilinear coordinates, you can use Macsyma (a separate Macsyma Inc. product) to write the PDEs automatically and pass them to PDEase for numerical solution.

39. Quantum Mechanics I next Next Contents. quantum mechanics I. Niels Walet, Fall 1998. Date July 10, 1998. Contents; 1. Introduction 1.1 Blackbody radiation; http://walet.phy.umist.ac.uk/QM/LectureNotes/

Next: Contents Quantum Mechanics I Niels Walet, Fall 1998 Date: July 10, 1998 Contents 1. Introduction 1.1 Black-body radiation 1.2 Photo-electric effect ... 8.2 Expectation value of and for the harmonic oscillator 8.3 The measurement process 8.3.1 Repeated measurements 9. Ladder operators 9.1 Harmonic oscillators ... 9.2 The operators and 9.3 Eigenfunctions of through ladder operations 9.4 Normalisation and Hermitean conjugates 10. Time dependent wave functions 10.1 correspondence between time-dependent and time-independent solutions 10.2 Superposition of time-dependent solutions ... 11.3 Solutions independent of and 11.4 The hydrogen atom 11.5 Now where does the probability peak? 11.6 Spherical harmonics 11.7 General solutions Email Niels.Walet@umist.ac.uk

40. Von Neumann Centennial Conference Von Neumann centennial conference. Budapest, Hungary; 1520 October 2003. http://www.math.bme.hu/~vonneumann/

Von Neumann Centennial Conference: Linear Operators and Foundations of Quantum Mechanics Budapest, Hungary, 15-20 October, 2003 Announcement General information about the conference General information for participants Schedule of the first day (including pictures) Schedule of the further days (including pictures) List of participants Co-organizers and sponsors         Updated on 4th January, 2004.

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