41. Quantum Mechanics I quantum mechanics I. Pictures of pioneers in quantum mechanics; Visual quantum mechanics A very good source for a discussion of QM on a first year level. http://walet.phy.umist.ac.uk/QM/

Quantum Mechanics I This web page contains links to information relating to the course quantum mechanics I. In the future I shall add links to example sheets, as well as other QM related information. Some external information related to QM Pictures of pioneers in quantum mechanics Visual quantum mechanics A very good source for a discussion of QM on a first year level. Time development of quantum mechanical systems Very interesting simulations! Some documents related to the course Lecture notes or a BIG postscript file. Example sheets Handouts Homework No. 2 due 27/11/98! Previous exams Mathematica material Summary of lectures last years summary You can also view an incomplete set of my lecture notes . This requires a browser that handles HTML 3.2 files. If you would like to ask questions, make suggestions, point out omisssions: I am always prepared to talk to you in person. Give me a call at 3693, or stop by my office (H9/4). You can also send me email at Niels.Walet@umist.ac.uk

42. Time Travelling Newton, Einstein, special relativity theory, quantum mechanics, equations, Lorentz factor, radius of Schwarzschild, wormholes, tunnel effect and parallel universe. http://users.pandora.be/vannoppen/science1.htm

Travelling through time... This page is based on a thesis of three students from the St-Gertrudisinstitute in Landen (B). Although I adapted and added some things myself, the major research is done by them. Please mail me before copying this. To see the printable version of these pages, click here I) Introduction Before 1905 there wasn't much to say about time. In the 17th century Newton defined time as something that continues, no matter what, without any link with reality and according to its own nature. Everybody believed that time had its influence on the environment, but if you believed that the environment had its influence on time, you really had to be mad! That changed in 1905 with Einstein's special relativity theory, in which he showed that time can be influenced. But this doesn't mean time can be changed in such a way that you can travel to the future or the past. That's what it's all about on this pages: Is it possible to travel through time, and if possible, under which circumstances? It will become very clear that the speed of light has got a major influence on the possibility of time travelling. An object should move faster than light speed to travel through time. Therefore we use the tunnel effect, an effect in the quantum mechanics. That means that a ray of light or a bundle of electrons that is sent through a certain barrier arrives sooner at the other side of the barrier than if there wasn't a barrier.

43. Quantum Mechanics Examples 5½ Examples in quantum mechanics. Index The new theories PAM Dirac (1930) Preface The Principles of quantum mechanics. We have always http://www.physics.csbsju.edu/QM/

Index The new theories, if one looks apart from their mathematical setting, are built up from physical concepts which cannot be explained in terms of things previously known to the student, which cannot even be explained adequately in words at all. Like the fundamental concepts (e.g., proximity, identity) which every one must learn on his arrival into the world, the newer concepts of physics can be mastered only by long familiarity with their properties and uses. P.A.M. Dirac (1930) Preface The Principles of Quantum Mechanics We have always had a great deal of difficulty understanding the world view that quantum mechanics represents. At least I do, because I'm an old enough man that I haven't got to the point that this stuff is obvious to me. Okay, I still get nervous with it... You know how it is, every new idea, it takes a generation or two until it becomes obvious that there's no real problem... I cannot define the real problem, therefore I suspect there's no real problem, but I'm not sure there's no real problem. R. P. Feynman as quoted in

44. Identity Of Indiscernibles Essay by Allan Randall, relating Leibinz's criterion to Everett's possible worlds semantics of quantum mechanics. http://home.ican.net/~arandall/Indiscernibles/

http://home.ican.net/~arandall/Indiscernibles/ Quantum Superposition, Necessity and the Identity of Indiscernibles Allan F. Randall Toronto, Ontario, Canada arandall@ican.net http://home.ican.net/~arandall/ Abstract Those who interpret quantum mechanics literally are forced to follow some variant of Everett's relative state formulation (or "many worlds" interpretation). It is generally assumed that this is a rather bizarre result that many physicists (especially cosmologists) have been forced into because of the evidence. I look at the history of philosophy, however, reveals that rationalism has always flirted with this very idea, from Parmenides to Leibniz to modern times. I will survey some of the philosophical history, and show how the so-called paradox of quantum superposition can be considered a consequence of basic rationalist assumptions such as the principle of sufficient reason and the identity of indiscernibles. I. Introduction Most physicists see quantum weirdness as something we have to accept in spite of ourselves, because of the overwhelming empirical evidence in its favour. Richard Feynman argued that we must simply admit that Nature makes no sense - knuckle under and accept the evidence, no matter how weird it seems ( Feynman 1985 Yet several hundred years ago Gottfried Wilhelm Leibniz came remarkably close to formulating an early version of Quantum Theory, without the benefit of any of the empirical evidence that aids us today. His Principle of the Identity of Indiscernibles states that no two different objects can have the same description (

45. Index For The Quantum Mechanics Examples Index for 5½ Examples in quantum mechanics. Home Page Falling Motion in a Linear Potential One Dimensional classical motion PE, turning points, z(t), etc. http://www.physics.csbsju.edu/QM/Index.html

Home Page Falling: Motion in a Linear Potential One Dimensional classical motion: PE, turning points, z(t) , etc. length and energy scales ... approximation methods: WKB, Rayleigh-Ritz (variational), perturbation theory Two Dimensional classical ballistic (projectile) motion separation of variables QM force-free motion: a moving lump of probability density visualizing the moving lump of probability density ... Problems Simple Harmonic Oscillator One Dimensional classical motion: PE, turning points, x(t) , etc. length and energy scales ... raising and lowering operators Two Dimensional xy 1D products, r : Laguerre polynomials degeneracy QM "motion": an orbiting wavefunction Three Dimensional xyz 1D products, r : Laguerre polynomials visualizing the wavefunctions in 3D WKB approximation in 3D Problems Hydrogen Atom classical motion: PE, turning points, Kepler's Laws, r(t) , etc. length and energy scales ... problems Square Wells One Dimensional classical motion: PE, turning points, x(t) , etc. length and energy scales ... square barrier: tunneling Two Dimensional infinite rectangular square-well: xy separation round square-well: Bessel functions ... scattering from round infinite barrier: phase shifts, cross-section

46. Bohm, Bell, And Boom! Quantum Mechanics And The End Of Modern Dualism From History and Philosophy of Science, Fall, 1997. By Dr. Ess. http://www.drury.edu/faculty/ess/philsci/bell.html

Notes on David Peat, Einstein's Moon: Bell's Theorem and the Curious Quest for Quantum Reality History and Philosophy of Science - Fall, 1997 - Dr. Ess Outline: "Bohm, Bell - and Boom! The End of Modern Dualism" The End of Cartesian Dualism: Physics (re)discovers Philosophy over against Cartesian and especially 19th ct. positivist dualisms which separate physics and philosophy - the emergence of quantum mechanics forces physicists to be become philosophers again. Indeed, the logic of complementarity which q.m. requires ripples into a larger (re)turn to complementary relationships between physics, philosophy, and religion. (In other terms: Cartesian dualism defines both 19th ct. positivism and fundamentalism as "mirror images" of one another: each agree that only one mode of knowing can be true - and the alternative mode(s) must be false: Positivism Fundamentalism ("calculative") reason (= natural science) "religion" "religion" reason/science The end of Cartesian dualism thus undermines the dualistic epistemologies of both positivism and fundamentalism.)

47. New Understandings Contains several essays. http://www.geocities.com/new_understandings/personalpage.html

Introduction In this site you will find essays I wrote where I will try to convey my ideas. I hope to give new, uncommon points of view which will stimulate the visitors to develope new outlooks. I will add more essays as the time allows me to do, so keep on visiting occasionally. I will be expecting to have your comments. Write whatever you feel like. Essays Home New Understandings

48. Tour Quantum Mechanics Personalities Quantum Theory Comes of Age. With a body from the outset. And some justification for the quantum results needed to be forthcoming. http://www.chembio.uoguelph.ca/educmat/chm386/rudiment/tourquan/tourquan.htm

Quantum Theory Comes of Age Niels Bohr - The Old Quantum Theory Louis de Broglie Wave Mechanics Werner Heisenberg ... Or you can escape from this tour Author: Dan Thomas email: Last Updated: Friday, July 5, 1996

49. Transgressing The Boundaries: Toward A Transformative Hermeneutics Of Quantum Gr Essay by physicist, Alan Sokal, teasing philosophical implications from quantum mechanics, with a view to accomodating some feminist and poststructuralist critiques of the ideology of domination perceived to be inherent in the discourse of much of the scientific community. http://www.physics.nyu.edu/faculty/sokal/transgress_v2/transgress_v2_singlefile.

Transgressing the Boundaries: Towards a Transformative Hermeneutics of Quantum Gravity Alan D. Sokal Department of Physics New York University 4 Washington Place New York, NY 10003 USA Internet: SOKAL@NYU.EDU Telephone: (212) 998-7729 Fax: (212) 995-4016 November 28, 1994 revised May 13, 1995 Note: This article was published in Social Text , pp. 217-252 (spring/summer 1996). Biographical Information: Random Walks, Critical Phenomena, and Triviality in Quantum Field Theory (Springer, 1992). Transgressing disciplinary boundaries ... [is] a subversive undertaking since it is likely to violate the sanctuaries of accepted ways of perceiving. Among the most fortified boundaries have been those between the natural sciences and the humanities. Valerie Greenberg, Transgressive Readings The struggle for the transformation of ideology into critical science ... proceeds on the foundation that the critique of all presuppositions of science and ideology must be the only absolute principle of science. Stanley Aronowitz

50. Rudiments Of Quantum Theory Though admittedly more complex, it is possible to follow a thread through the last four centuries up to the birth of modern quantum mechanics. http://www.chembio.uoguelph.ca/educmat/chm386/rudiment/rudiment.htm

Rudiments of Quantum Theory Quantum theory was not created "out of the blue". It's mathematical framework and ideas grow out of a long history of classical mechanics. A number of certain experiments around the turn of the century created the need to replace the classical theory of matter with a new quantum theory. The first attempt's (Bohr) had remarkable yet limited success. This became known as the Old Quantum Theory. Classical Tour Experimental Tour Quantum Tour Mathematical Basics ... Simple Quantum Models An important aspect of understanding of one's position is to appreciate where one came from. This is also true of modern science. Though admittedly more complex, it is possible to follow a thread through the last four centuries up to the birth of modern quantum mechanics. Rene Descartes is often credited as the Father of Modern Mathematics. While a mercenary soldier, he experienced a dream one night that triggered in his mind the idea of modern algebra. (Some nightmare!) It is helpful to follow a short tour from Descartes through to Newton, Bernoulli, Euler, Hamilton, Maxwell, Einstein, Schrodinger, Heisenberg, and Dirac. It is revealing to see how the mathematical ideas of one generation opened new avenues for the next.

51. ALCHEMICAL OCTAVES This is a fascinating look at the deeper structure of reality based on alchemical octave theory. From music to DNA, from the emerald formula to quantum mechanics, this is the intrinsic pattern that the universe follows. http://www.angelfire.com/hi2/UFOCHARTS/index.html

52. Quantum Chemistry quantum mechanics methods are based on the following principles Nuclei and electrons are distinguished from each other. Electron http://cmm.info.nih.gov/modeling/guide_documents/quantum_mechanics_document.html

Note that definitions of many of the acronyms used in this document can be found in the Quantum Chemistry Acronyms Database (Northern Illinois Univ.). Quantum Chemistry Quantum theory is based on Schrodinger's equation: in which electrons are considered as wave-like particles whose "waviness" is mathematically represented by a set of wavefunctions obtained by solving Schrodinger's equation. Schrodinger's equation addresses the following questions: Where are the electrons and nuclei of a molecule in space? configuration, conformation, size, shape, etc. Under a given set of conditions, what are their energies? heat of formation, conformational stability, chemical reactivity, spectral properties, etc. Schrodinger's equation for molecular systems can only be solved approximately. The approximation methods can be categorized as either ab initio or semiempirical . Semiempirical methods use parameters that compensate for neglecting some of the time consuming mathematical terms in Schrodinger's equation, whereas ab initio methods include all such terms. The parameters used by semiempirical methods can be derived from experimental measurements or by performing

53. APS Manuscripts Department Located in Philadelphia, Pennsylvania. A collection which dates from the Society's founding in 1743. Includes first editions of Sir Isaac Newton's 'Principia' and Charles Darwin's 'Origin of Species.' Areas of particular strength 18th and 19th century natural history, the history of genetics and eugenics in America, quantum mechanics, and the development of cultural anthropology in America. Research grants and fellowships are available. Research affiliation Research Library Group. http://www.amphilsoc.org/library/

Your browser does not support script American Philosophical Society Library Home Members Meetings Publications Grants Overview of the Library Collections Peter Stephen Duponceau (1760-1844), APS 1791 The American Philosophical Society Library is a major national center for research in the history of the sciences, medicine, and technology. With its roots extending back to the founding of the Society in 1743, it houses over 300,000 volumes and bound periodicals, eight million manuscripts, 100,000 images, and thousands of hours of audio tape. Among the many extraordinary books in the collections of printed materials are first editions of Sir Isaac Newton's Principia , Charles Darwin's Origin of Species , a presentation copy of Thomas Jefferson's Notes on the State of Virginia , the elephant folio of Audubon's Birds of North America (for which the A.P.S. was an original subscriber), as well as a majority of Benjamin Franklin imprints and a significant portion of Franklin's personal library. Manuscript collections range from eighteenth-century natural history, American Indian linguistics and culture , to nuclear physics, computer development, and medical science . The Library is among the premier institutions in the nation for documenting the history of genetics and eugenics , the study of natural history in the 18th and 19th centuries, quantum mechanics , and the development of cultural anthropology in America.

54. The Transactional Interpretation Of Quantum Mechanics The Transactional Interpretation of quantum mechanics. John G. Cramer. ABSTRACT. The interpretational problems of quantum mechanics are considered. http://www.npl.washington.edu/npl/int_rep/tiqm/TI_toc.html

The Transactional Interpretation of Quantum Mechanics John G. Cramer Department of Physics University of Washington PO Box 351560 Seattle WA 98195-1560 USA This paper was originally published in Reviews of Modern Physics See also "Generalized absorber theory and the Einstein-Podolsky-Rosen paradox", published in Physical Review D "An Overview of the Transactional Interpretation of Quantum Mechanics", published in the International Journal of Theoretical Physics , 227 (1988), and "Velocity Reversal and the Arrow of Time" , published in Foundations of Physics Note: Some browsers seem to fail in printing this paper from the HTML files. Therefore, PostScript versions of these pages are being made available in a separate directory. ABSTRACT P= ], basic elements of the CI. Table of Contents 1.0 Introduction 1.0.1 Contrafactual Definiteness 1.0.2 Nonlocality and Formalism 1.0.3 Overview of Contents ... Continue to Section 1.0 This page was created by John G. Cramer on 7/1/96. It now has an access count of:

55. Quantum Mechanics Introduction Back to Contents. http://www.7stones.com/Homepage/Publisher/QM.html

Back to Contents. Back to Contents.

56. Edward Witten, Institute For Advanced Study (Princeton), Duality, Spacetime And Schedule Duality, Spacetime and quantum mechanics. Edward Witten, Institute for Advanced Study (Princeton). In the last few years, physicists http://online.itp.ucsb.edu/online/plecture/witten/

Schedule Duality, Spacetime and Quantum Mechanics Edward Witten , Institute for Advanced Study (Princeton) In the last few years, physicists have learned that the different string theories discovered and studied in different ways are limiting cases of a single, more powerful theory, known as M theory. "M" stands for magic, mystery, or matrix, according to taste. Some of these developments will be explained in this lecture. Edward Witten, professor of physics at the Institute for Advanced Study in Princeton, N.J., is arguably the premier theoretical physicist of our time. Renowned for his many contributions to particle physics and string theory, Witten has almost single-handedly constructed a new branch of mathematical physics For his achievements, he has been awarded mathematics' highest prize, the 1990 Fields Medal. A member of the National Academy of Sciences, he is a recipient of a MacArthur Prize, the Dirac Medal, and many other honors. Audio for this talk requires sound hardware, and RealPlayer or RealAudio by RealNetworks.

57. Many-Worlds Interpretation Of Quantum Mechanics Interpretation of quantum mechanics due to Hugh Everett according to which many universes exist in parallel at the same space and time; by Lev Vaidman. http://plato.stanford.edu/entries/qm-manyworlds/

version history HOW TO CITE THIS ENTRY Stanford Encyclopedia of Philosophy A B C D ... Z This document uses XHTML-1/Unicode to format the display. Older browsers and/or operating systems may not display the formatting correctly. last substantive content change MAR Many-Worlds Interpretation of Quantum Mechanics The Many-Worlds Interpretation (MWI) is an approach to quantum mechanics according to which, in addition to the world we are aware of directly, there are many other similar worlds which exist in parallel at the same space and time. The existence of the other worlds makes it possible to remove randomness and action at a distance from quantum theory and thus from all physics. 1. Introduction 2. Definitions 2.1 What is "A World"? 2.2 Who am "I"? ... Related Entries 1. Introduction The fundamental idea of the MWI, going back to Everett 1957 , is that there are myriads of worlds in the Universe in addition to the world we are aware of. In particular, every time a quantum experiment with different outcomes with non-zero probability is performed, all outcomes are obtained, each in a different world, even if we are aware only of the world with the outcome we have seen. In fact, quantum experiments take place everywhere and very often, not just in physics laboratories: even the irregular blinking of an old fluorescent bulb is a quantum experiment. There are numerous variations and reinterpretations of the original Everett proposal, most of which are briefly discussed in the entry on

58. KryssTal : An Introduction To Quantum Mechanics An Introduction to quantum mechanics. A beginners (nonmathematical) guide to the strange world of the atom. Part Two - quantum mechanics. http://www.krysstal.com/quantum.html

An Introduction to Quantum Mechanics A beginners' (non-mathematical) guide to the strange world of the atom Part One - The Story of The Atom In the essay on Relativity , I stated that the Theory of Relativity was one of the two most important ideas of 20th Century science. Relativity is a deviation from Newtonian Mechanics (also known as common sense!). The deviations were not discovered until this Century because they are only noticeable at high speeds and under very intense gravitational fields. There is another 20th Century idea that also violates Newtonian Mechanics. This is called Quantum Mechanics. In this essay I will give a taste of the strange and fascinating world of the atom. I will try to keep it general and simple because these ideas are even more weird than Relativity (if that is possible). The Ancient Greeks proposed that matter could not be divided indefinitely. They speculated that matter was made up of units called atoms . The word comes from a Greek word meaning single item or portion . They assumed that atoms were solid, different characteristics of substances being determined by the different shapes that atoms had. This atomic idea never really became popular.

59. Mark J Hadley Measurement changes toplogy of the spacetime. http://www.warwick.ac.uk/~phsem/

Dr. Mark J. Hadley, Department of Physics, University of Warwick, Coventry CV4 7AL, UK Office: P557 Tel: +44(0)24 765 24263 Fax: +44 (0)24 765 8409 Email: Mark.Hadley@warwick.ac.uk Dr. Mark J. Hadley A Gravitational Explanation for Quantum Mechanics My work offers an explanation for quantum phenomena in terms of classical general relativity. Far from being incompatible the two great theories of the 20th century are shown to be closely related. Quantum theory gives clues to the small scale structure of space and time through the EPR experiments and the Kochen Specker paradox. In return general relativity can account for the strange effects seen in quantum theory. The crucial link is a relaxation of the strict causal structure that is normally imposed upon Einstein's theory, but which forms no part of the mathematical structure. This controversial work contrasts with the mainstream view that the theories are incompatible - with the favoured remedy being to discard general relativity and replace it with a quantum theory of gravity. Popular Reports There have been numerous reports of my work in Science magazines, local and national press. The most comprehensive article is:

60. VQM Redirect Visual quantum mechanics Physics Education Research Group. You will be redirected to the new homepage of Visual quantum mechanics in 5 seconds. http://www.phys.ksu.edu/perg/vqm/

Visual Quantum Mechanics Physics Education Research Group Kansas State University You will be redirected to the new homepage of Visual Quantum Mechanics in seconds. If you cannot wait that long, click here

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