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Unit 1 Old Quantum Theory
UNIT 1 OLD QUANTUM THEORY Structure Introduction Objectives li;,:overy of Sub-atomic Particles Earlier Atom Models Light as clectromagnetic Wave Failures of Classical Physics Black Body Radiation '1 Heat Capacity Variation Photoelectric Effect Atomic Spectra Planck's Quantum Theory, Black Body ~diation. and Heat Capacity Variation Einstein's Theory of Photoelectric Effect Bohr Atom Model Calculation of Radius of Orbits Energy of an Electron in an Orbit Atomic Spectra and Bohr's Theory Critical Analysis of Bohr's Theory Refinements in the Atomic Spectra The61-y Summary Terminal Questions Answers 1.1 INTRODUCTION The ideas of classical mechanics developed by Galileo, Kepler and Newton, when applied to atomic and molecular systems were found to be inadequate. Need was felt for a theory to describe, correlate and predict the behaviour of the sub-atomic particles. The quantum theory, proposed by Max Planck and applied by Einstein and Bohr to explain different aspects of behaviour of matter, is an important milestone in the formulation of the modern concept of atom. In this unit, we will study how black body radiation, heat capacity variation, photoelectric effect and atomic spectra of hydrogen can be explained on the basis of theories proposed by Max Planck, Einstein and Bohr. They based their theories on the postulate that all interactions between matter and radiation occur in terms of definite packets of energy, known as quanta. Their ideas, when extended further, led to the evolution of wave mechanics, which shows the dual nature of matter -
Arxiv:1206.1084V3 [Quant-Ph] 3 May 2019
Overview of Bohmian Mechanics Xavier Oriolsa and Jordi Mompartb∗ aDepartament d'Enginyeria Electr`onica, Universitat Aut`onomade Barcelona, 08193, Bellaterra, SPAIN bDepartament de F´ısica, Universitat Aut`onomade Barcelona, 08193 Bellaterra, SPAIN This chapter provides a fully comprehensive overview of the Bohmian formulation of quantum phenomena. It starts with a historical review of the difficulties found by Louis de Broglie, David Bohm and John Bell to convince the scientific community about the validity and utility of Bohmian mechanics. Then, a formal explanation of Bohmian mechanics for non-relativistic single-particle quantum systems is presented. The generalization to many-particle systems, where correlations play an important role, is also explained. After that, the measurement process in Bohmian mechanics is discussed. It is emphasized that Bohmian mechanics exactly reproduces the mean value and temporal and spatial correlations obtained from the standard, i.e., `orthodox', formulation. The ontological characteristics of the Bohmian theory provide a description of measurements in a natural way, without the need of introducing stochastic operators for the wavefunction collapse. Several solved problems are presented at the end of the chapter giving additional mathematical support to some particular issues. A detailed description of computational algorithms to obtain Bohmian trajectories from the numerical solution of the Schr¨odingeror the Hamilton{Jacobi equations are presented in an appendix. The motivation of this chapter is twofold. -
Rutherford's Nuclear World: the Story of the Discovery of the Nuc
Rutherford's Nuclear World: The Story of the Discovery of the Nuc... http://www.aip.org/history/exhibits/rutherford/sections/atop-physic... HOME SECTIONS CREDITS EXHIBIT HALL ABOUT US rutherford's explore the atom learn more more history of learn about aip's nuclear world with rutherford about this site physics exhibits history programs Atop the Physics Wave ShareShareShareShareShareMore 9 RUTHERFORD BACK IN CAMBRIDGE, 1919–1937 Sections ← Prev 1 2 3 4 5 Next → In 1962, John Cockcroft (1897–1967) reflected back on the “Miraculous Year” ( Annus mirabilis ) of 1932 in the Cavendish Laboratory: “One month it was the neutron, another month the transmutation of the light elements; in another the creation of radiation of matter in the form of pairs of positive and negative electrons was made visible to us by Professor Blackett's cloud chamber, with its tracks curled some to the left and some to the right by powerful magnetic fields.” Rutherford reigned over the Cavendish Lab from 1919 until his death in 1937. The Cavendish Lab in the 1920s and 30s is often cited as the beginning of modern “big science.” Dozens of researchers worked in teams on interrelated problems. Yet much of the work there used simple, inexpensive devices — the sort of thing Rutherford is famous for. And the lab had many competitors: in Paris, Berlin, and even in the U.S. Rutherford became Cavendish Professor and director of the Cavendish Laboratory in 1919, following the It is tempting to simplify a complicated story. Rutherford directed the Cavendish Lab footsteps of J.J. Thomson. Rutherford died in 1937, having led a first wave of discovery of the atom. -
Walther Nernst, Albert Einstein, Otto Stern, Adriaan Fokker
Walther Nernst, Albert Einstein, Otto Stern, Adriaan Fokker, and the Rotational Specific Heat of Hydrogen Clayton Gearhart St. John’s University (Minnesota) Max-Planck-Institut für Wissenschaftsgeschichte Berlin July 2007 1 Rotational Specific Heat of Hydrogen: Widely investigated in the old quantum theory Nernst Lorentz Eucken Einstein Ehrenfest Bohr Planck Reiche Kemble Tolman Schrödinger Van Vleck Some of the more prominent physicists and physical chemists who worked on the specific heat of hydrogen through the mid-1920s. See “The Rotational Specific Heat of Molecular Hydrogen in the Old Quantum Theory” http://faculty.csbsju.edu/cgearhart/pubs/sel_pubs.htm (slide show) 2 Rigid Rotator (Rotating dumbbell) •The rigid rotator was among the earliest problems taken up in the old (pre-1925) quantum theory. • Applications: Molecular spectra, and rotational contri- bution to the specific heat of molecular hydrogen • The problem should have been simple Molecular • relatively uncomplicated theory spectra • only one adjustable parameter (moment of inertia) • Nevertheless, no satisfactory theoretical description of the specific heat of hydrogen emerged in the old quantum theory Our story begins with 3 Nernst’s Heat Theorem Walther Nernst 1864 – 1941 • physical chemist • studied with Boltzmann • 1889: lecturer, then professor at Göttingen • 1905: professor at Berlin Nernst formulated his heat theorem (Third Law) in 1906, shortly after appointment as professor in Berlin. 4 Nernst’s Heat Theorem and Quantum Theory • Initially, had nothing to do with quantum theory. • Understand the equilibrium point of chemical reactions. • Nernst’s theorem had implications for specific heats at low temperatures. • 1906–1910: Nernst and his students undertook extensive measurements of specific heats of solids at low (down to liquid hydrogen) temperatures. -
Download Report 2010-12
RESEARCH REPORt 2010—2012 MAX-PLANCK-INSTITUT FÜR WISSENSCHAFTSGESCHICHTE Max Planck Institute for the History of Science Cover: Aurora borealis paintings by William Crowder, National Geographic (1947). The International Geophysical Year (1957–8) transformed research on the aurora, one of nature’s most elusive and intensely beautiful phenomena. Aurorae became the center of interest for the big science of powerful rockets, complex satellites and large group efforts to understand the magnetic and charged particle environment of the earth. The auroral visoplot displayed here provided guidance for recording observations in a standardized form, translating the sublime aesthetics of pictorial depictions of aurorae into the mechanical aesthetics of numbers and symbols. Most of the portait photographs were taken by Skúli Sigurdsson RESEARCH REPORT 2010—2012 MAX-PLANCK-INSTITUT FÜR WISSENSCHAFTSGESCHICHTE Max Planck Institute for the History of Science Introduction The Max Planck Institute for the History of Science (MPIWG) is made up of three Departments, each administered by a Director, and several Independent Research Groups, each led for five years by an outstanding junior scholar. Since its foundation in 1994 the MPIWG has investigated fundamental questions of the history of knowl- edge from the Neolithic to the present. The focus has been on the history of the natu- ral sciences, but recent projects have also integrated the history of technology and the history of the human sciences into a more panoramic view of the history of knowl- edge. Of central interest is the emergence of basic categories of scientific thinking and practice as well as their transformation over time: examples include experiment, ob- servation, normalcy, space, evidence, biodiversity or force. -
Feynman Quantization
3 FEYNMAN QUANTIZATION An introduction to path-integral techniques Introduction. By Richard Feynman (–), who—after a distinguished undergraduate career at MIT—had come in as a graduate student to Princeton, was deeply involved in a collaborative effort with John Wheeler (his thesis advisor) to shake the foundations of field theory. Though motivated by problems fundamental to quantum field theory, as it was then conceived, their work was entirely classical,1 and it advanced ideas so radicalas to resist all then-existing quantization techniques:2 new insight into the quantization process itself appeared to be called for. So it was that (at a beer party) Feynman asked Herbert Jehle (formerly a student of Schr¨odinger in Berlin, now a visitor at Princeton) whether he had ever encountered a quantum mechanical application of the “Principle of Least Action.” Jehle directed Feynman’s attention to an obscure paper by P. A. M. Dirac3 and to a brief passage in §32 of Dirac’s Principles of Quantum Mechanics 1 John Archibald Wheeler & Richard Phillips Feynman, “Interaction with the absorber as the mechanism of radiation,” Reviews of Modern Physics 17, 157 (1945); “Classical electrodynamics in terms of direct interparticle action,” Reviews of Modern Physics 21, 425 (1949). Those were (respectively) Part III and Part II of a projected series of papers, the other parts of which were never published. 2 See page 128 in J. Gleick, Genius: The Life & Science of Richard Feynman () for a popular account of the historical circumstances. 3 “The Lagrangian in quantum mechanics,” Physicalische Zeitschrift der Sowjetunion 3, 64 (1933). The paper is reprinted in J. -
The Concept of the Photon—Revisited
The concept of the photon—revisited Ashok Muthukrishnan,1 Marlan O. Scully,1,2 and M. Suhail Zubairy1,3 1Institute for Quantum Studies and Department of Physics, Texas A&M University, College Station, TX 77843 2Departments of Chemistry and Aerospace and Mechanical Engineering, Princeton University, Princeton, NJ 08544 3Department of Electronics, Quaid-i-Azam University, Islamabad, Pakistan The photon concept is one of the most debated issues in the history of physical science. Some thirty years ago, we published an article in Physics Today entitled “The Concept of the Photon,”1 in which we described the “photon” as a classical electromagnetic field plus the fluctuations associated with the vacuum. However, subsequent developments required us to envision the photon as an intrinsically quantum mechanical entity, whose basic physics is much deeper than can be explained by the simple ‘classical wave plus vacuum fluctuations’ picture. These ideas and the extensions of our conceptual understanding are discussed in detail in our recent quantum optics book.2 In this article we revisit the photon concept based on examples from these sources and more. © 2003 Optical Society of America OCIS codes: 270.0270, 260.0260. he “photon” is a quintessentially twentieth-century con- on are vacuum fluctuations (as in our earlier article1), and as- Tcept, intimately tied to the birth of quantum mechanics pects of many-particle correlations (as in our recent book2). and quantum electrodynamics. However, the root of the idea Examples of the first are spontaneous emission, Lamb shift, may be said to be much older, as old as the historical debate and the scattering of atoms off the vacuum field at the en- on the nature of light itself – whether it is a wave or a particle trance to a micromaser. -
Theory and Experiment in the Quantum-Relativity Revolution
Theory and Experiment in the Quantum-Relativity Revolution expanded version of lecture presented at American Physical Society meeting, 2/14/10 (Abraham Pais History of Physics Prize for 2009) by Stephen G. Brush* Abstract Does new scientific knowledge come from theory (whose predictions are confirmed by experiment) or from experiment (whose results are explained by theory)? Either can happen, depending on whether theory is ahead of experiment or experiment is ahead of theory at a particular time. In the first case, new theoretical hypotheses are made and their predictions are tested by experiments. But even when the predictions are successful, we can’t be sure that some other hypothesis might not have produced the same prediction. In the second case, as in a detective story, there are already enough facts, but several theories have failed to explain them. When a new hypothesis plausibly explains all of the facts, it may be quickly accepted before any further experiments are done. In the quantum-relativity revolution there are examples of both situations. Because of the two-stage development of both relativity (“special,” then “general”) and quantum theory (“old,” then “quantum mechanics”) in the period 1905-1930, we can make a double comparison of acceptance by prediction and by explanation. A curious anti- symmetry is revealed and discussed. _____________ *Distinguished University Professor (Emeritus) of the History of Science, University of Maryland. Home address: 108 Meadowlark Terrace, Glen Mills, PA 19342. Comments welcome. 1 “Science walks forward on two feet, namely theory and experiment. ... Sometimes it is only one foot which is put forward first, sometimes the other, but continuous progress is only made by the use of both – by theorizing and then testing, or by finding new relations in the process of experimenting and then bringing the theoretical foot up and pushing it on beyond, and so on in unending alterations.” Robert A. -
Quantum Mechanics I - Iii
QUANTUM MECHANICS I - III PHYS 516 - 518 Jan 1 - Dec. 31, 2015 Prof. R. Gilmore 12-918 X-2779 [email protected] office hours: 2:00 ! \1" Course Schedule: (Winter Quarter) MWF 11:00 - 11:50, Disque 919 Objective: To provide the foundations for modern physics. Course Requirements and Obligations Course grading will be based on assigned homework problem sets and a midterm and final exam. Texts Two texts and one supplement will be used for this course. The first text has been chosen from among many admirable texts because it provides a more comprehensive treatment of quantum physics discovered since 1970 than other texts. The second text will be used primarily during the second quarter of this course (PHYS517). It provides hands-on experience for solving binding and scattering problems in one dimension and potentials involving periodic poten- tials, again in one dimension. The third text (optional) is strongly recommended for those who feel their undergratuate experience in this beautiful subject may be deficient in some way. It is out of print but a limited number of copies are often available through Amazon in the event our book store has sold out of their reprinted copies. 1 David H. McIntyre Quantum Mechanics NY: Pearson, 2012 ISBN-10: 0-321-76579-6 R. Gilmore Elementary Quantum Mechanics in One Dimension Baltimore, Johns Hopkins University Press, 2004 ISBN 0-8018-8015-7 R. H. Dicke and J. P. Wittke Introduction to Quantum Mechanics Reading, MA: Addison-Wesley, 1960 ISBN 0-? If it becomes a hardship to acquire this fine text, you can get about the same information from another, later, fine text: David J. -
Memorial Tributes: Volume 15
THE NATIONAL ACADEMIES PRESS This PDF is available at http://nap.edu/13160 SHARE Memorial Tributes: Volume 15 DETAILS 444 pages | 6 x 9 | HARDBACK ISBN 978-0-309-21306-6 | DOI 10.17226/13160 CONTRIBUTORS GET THIS BOOK National Academy of Engineering FIND RELATED TITLES Visit the National Academies Press at NAP.edu and login or register to get: – Access to free PDF downloads of thousands of scientific reports – 10% off the price of print titles – Email or social media notifications of new titles related to your interests – Special offers and discounts Distribution, posting, or copying of this PDF is strictly prohibited without written permission of the National Academies Press. (Request Permission) Unless otherwise indicated, all materials in this PDF are copyrighted by the National Academy of Sciences. Copyright © National Academy of Sciences. All rights reserved. Memorial Tributes: Volume 15 Memorial Tributes NATIONAL ACADEMY OF ENGINEERING Copyright National Academy of Sciences. All rights reserved. Memorial Tributes: Volume 15 Copyright National Academy of Sciences. All rights reserved. Memorial Tributes: Volume 15 NATIONAL ACADEMY OF ENGINEERING OF THE UNITED STATES OF AMERICA Memorial Tributes Volume 15 THE NATIONAL ACADEMIES PRESS Washington, D.C. 2011 Copyright National Academy of Sciences. All rights reserved. Memorial Tributes: Volume 15 International Standard Book Number-13: 978-0-309-21306-6 International Standard Book Number-10: 0-309-21306-1 Additional copies of this publication are available from: The National Academies Press 500 Fifth Street, N.W. Lockbox 285 Washington, D.C. 20055 800–624–6242 or 202–334–3313 (in the Washington metropolitan area) http://www.nap.edu Copyright 2011 by the National Academy of Sciences. -
Chapter 2 Quantum Theory
Chapter 2 - Quantum Theory At the end of this chapter – the class will: Have basic concepts of quantum physical phenomena and a rudimentary working knowledge of quantum physics Have some familiarity with quantum mechanics and its application to atomic theory Quantization of energy; energy levels Quantum states, quantum number Implication on band theory Chapter 2 Outline Basic concept of quantization Origin of quantum theory and key quantum phenomena Quantum mechanics Example and application to atomic theory Concept introduction The quantum car Imagine you drive a car. You turn on engine and it immediately moves at 10 m/hr. You step on the gas pedal and it does nothing. You step on it harder and suddenly, the car moves at 40 m/hr. You step on the brake. It does nothing until you flatten the brake with all your might, and it suddenly drops back to 10 m/hr. What’s going on? Continuous vs. Quantization Consider a billiard ball. It requires accuracy and precision. You have a cue stick. Assume for simplicity that there is no friction loss. How fast can you make the ball move using the cue stick? How much kinetic energy can you give to the ball? The Newtonian mechanics answer is: • any value, as much as energy as you can deliver. The ball can be made moving with 1.000 joule, or 3.1415926535 or 0.551 … joule. Supposed it is moving with 1-joule energy, you can give it an extra 0.24563166 joule by hitting it with the cue stick by that amount of energy. -
Quantum Mechanics of the Electron Particle-Clock
Quantum Mechanics of the electron particle-clock David Hestenes Department of Physics, Arizona State University, Tempe, Arizona 85287-1504∗ Understanding the electron clock and the role of complex numbers in quantum mechanics is grounded in the geometry of spacetime, and best expressed with Spacetime Algebra (STA). The efficiency of STA is demonstrated with coordinate-free applications to both relativistic and non- relativistic QM. Insight into the structure of Dirac theory is provided by a new comprehensive analysis of local observables and conservation laws. This provides the foundation for a comparative analysis of wave and particle models for the hydrogen atom, the workshop where Quantum Mechanics was designed, built and tested. PACS numbers: 10,03.65.-w Keywords: pilot waves, zitterbewegung, spacetime algebra I. INTRODUCTION The final Section argues for a realist interpretation of the Dirac wave function describing possible particle De Broglie always insisted that Quantum Mechanics is paths. a relativistic theory. Indeed, it began with de Broglie`s relativistic model for an electron clock. Ironically, when Schr¨odingerintroduced de Broglie`s idea into his wave II. SPACETIME ALGEBRA equation, he dispensed with both the clock and the rela- tivity! Spacetime Algebra (STA) plays an essential role in the This paper aims to revitalize de Broglie's idea of an formulation and analysis of electron theory in this paper. electron clock by giving it a central role in physical inter- Since thorough expositions of STA are available in many pretation of the Dirac wave function. In particular, we places [2{4], a brief description will suffice here, mainly aim for insight into structure of the wave function and to establish notations and define terms.