Johns Hopkins, MATH 443

Excerpt: ... LECTURE 25. THE HEISENBERG UNCERTAINTY PRINCIPLE FOURIER ANALYSIS (110.443) PROF. QIAO ZHANG 1. The Mathematical Formulation Theorem 1.1 ( Heisenberg Uncertainty Principle ). Let S (R), so normalized that 2 = 1. Then we have (1.1) - x2 |(x)|2 dx - ^ 2 |()|2 d 1 . 16 2 The equality holds true if and only if (1.2) for some B > 0 and R. Corollary 1.2. Let S (R), so normalized that Then we have 2 (x) = 4 2B -Bx2 +i e = 1, and let x0 , 0 R. 1 . 16 2 (1.3) - (x - x0 )2 |(x)|2 dx - ^ ( - 0 )2 |()|2 d 2. The Physical Formulation The Heisenberg uncertainty principle originated from the study of quantum mechanics. In quantum mechanics, every matter has two identities, both as particles and as waves, and its state is governed by the so-called state function, or wave function, . In particular, if we let x0 = - x|(x)|2 dx, 0 = - ^ |()|2 d, then the two integrals (x - x0 )2 |(x)|2 dx, - - ^ ( - 0 )2 |()|2 d respectively represent the uncertainties of our measurements of the position ...

Rutgers, CHEM 327

Excerpt: ... EXAM I MATERIAL ExamI on Monday, October 4, will cover the material in Chapter 18: Sections 1-11, 16 and 17. You may ignore the "derivation" of the Heisenberg Uncertainty Principle on pages 605/606; the "derivation" involving the time-independent vs. time-dependent SE's on pages 612/613. You should know, however, what the Heisenberg Uncertainty Principle is, what "stationary states" are and why they are called "stationary" (eq. 18.25). From Section 16, you need to know (and be able to use) the properties of Hermitian operators.ignore proofs and the sub-section on "Complete Sets". The Exam will be offered during the regular Lecture period. Please, be prompt and bring a calculator.a calculator that works .:-) ...

UCLA, CHEM 113A

Excerpt: ... Preview #15 (Chem113A W09, due Mon. 2/9/09 at 12:05pm in class) Attendance record: I am [ ] present at or [ Assigned reading: Engel 6.36.4 ] absent from this class meeting (see date and time above). Name:_ Forming study groups is permissible, but you must construct your solutions independently. By writing down my name, I confirm that I strictly obey the academic ethic code when doing this preview and my statement on attendance (above) is correct. Please write down the names of everyone who you worked with on this preview in the space above. [1] Heisenberg Uncertainty Principle . [1](a) Please calculate x, the uncertainty in position x, for a particle (mass m) in a 1D box with length L at n=2 eigenstate. Please show algebraic details; do not just plug the numbers into the formula on p. 91. [1](b) Same as [1](a), but please calculate p , the uncertainty in linear momentum p. Please show algebraic details; do not just plug the numbers into the formula on p. 91. [1](c) Based o ...

Case Western Reserve University, ENGR 145

Excerpt: ... Lecture 3 Atomic Theory II From the Bohr model to Schrdinger's wave equation Reading assignment: OGC 4.4-4.5, 5.1, 5.3-5.4 Learning objectives: Recognize the wave-particle duality of electrons Understand consequences of the Schrdinger equation: the shape of electron orbitals in atoms the electronic configurations of atoms the form of the periodic table of the elements Know how the Heisenberg uncertainty principle limits the precision with which we can know something's position, momentum, and energy Lecture 3, spring 2009 ENGR 145: Chemistry of Materials Case Western Reserve University Wave Nature of Matter (OGC 4.4) Some classical physical systems have quantized states and a wave nature, e.g the standing wave of a vibrating string: n = L, 2 = 1,2,3,. DeBroglie: If energy of an e in a Bohr radius has quantized energy, does it also have a wavelength? 4.17 Lecture 3, spring 2009 ENGR 145: Chemistry of Materials Case Western Reserve University De Broglie Wavelength of Electr ...

Purdue, CHM 370

Excerpt: ... Problem Set3 Due date : September 19, 2008 Fundamental Uncertainty Q#1. The Heisenberg Uncertainty Principle (HUP) was initially developed in the late 1920s as a result of Heisenbergs matrix mechanics. Heisenbergs original paper in 1927 applied his theory exclusively to particles (a.k.a. matter waves) but the theory is fundamental property of all waves including acoustic waves. Lets explore the consequences of the HUP using this much more familiar system. By using the WRITEWAV command in MathCAD we can demonstrate the relationship between time and position and actually hear the effects of the HUP. Starting with the MathCAD file that you should have received in the same emails as this homework assignment (if you do not have it, it will be posted on the class website). This source file contains all the parameters needed to write *.wav files directly from a mathematically generated array. a) Our textbook and the derivation in class introduced the Heisenberg Uncertainty Principle as a position ...

JMU, HONORS 200

Excerpt: ... HON200D/REL300-04Study Guide for Test IIPruett2004 1 General Comments The primary purposes of Test II are to 1) check that you have done the required reading, and 2) to help you process and assimilate some conceptually difficult ideas. For the lat ...

Bucknell, PHYS 141

Excerpt: ... Hello Physics 141 Students. Assignment and Notes for 11/22/02 (class 37): READ Great Ideas in Physics, Chapter 4, pp. 207-240 and the file QUANTUM THEORY OF FIELDS. This seems like a lot, but you will be skimming or skipping much of it. Details below. READ pp. 207-211. This includes the sections on The Heisenberg Uncertainty Principle and the Demise of Determinism in Science (pp. 207-208), Determinism in Prequantum Physics (pp. 208-210) and The Basic Idea of the Principle (pp. 210-211). You can stop at Spreading Out of Light as a Wave. SKIM/SKIP pp. 212-224. You should already have read pp. 225-227 on the de Broglie Relation. READ pp. 227-236. This includes the sections on the Heisenberg Uncertainty Principle (pp. 227-231), the examples Molecules Through a Hole and Predictability in the Quantum World (pp. 231-236), and Quantum Mechanics (p. 236) READ pp. 236-240, Determinism, Causality, and Choice in the Quantum World. READ the file entitled QUANTUM THEORY OF FIELDS, available at the course website, under ...

Christian Brothers, P 252

Excerpt: ... should be able to test this wave behavior via interference and diffraction. In fact, experiments show that electrons DO EXHIBIT INTERFERENCE when they go through multiple slits, just as the DeBroglie Hypothesis indicates. DeBroglie Hypothesis Even neutrons have shown interference phenomena when they are diffracted from a crystal structure according to the DeBroglie Hypothesis: = h/p . Note that h is very small, so that normally will also be very small (unless the mv is also very small). A small means very little diffraction effects [1.22 = D sin()]. Quantum Theory What we are now dealing with is the Quantum Theory: atoms are quantized (you can have 2 or 3, but not 2.5 atoms) light is quantized (you can have 2 or 3 photons, but not 2.5) in addition, we have quantum numbers (L = nr , where n is an integer) Heisenberg Uncertainty Principle There is a major problem with the wave/particle duality: a) a wave with a definite frequency and wavelength (e.g., a nice sine wave) does not have a definite ...

Allan Hancock College, PHYS 1002

Excerpt: ... PHYS1002 Tutorial Sheet No. 6 To help celebrate CERN's 50th anniversary this year, the Particle Physics and Astronomy Research Council (PPARC) has produced a screensaver featuring the Large Hadron Collider (LHC). Due to open in 2007, the LHC will be the world's most powerful particle accelerator. Physicists hope it will reveal the origin of mass, new supersymmetric particles and perhaps even the existence of extra, hidden dimensions of space. The screensaver can be downloaded from the PPARC CERN 50th anniversary web page, where you can also see the amazing CERN fact of the week, at http:/www.pparc.ac.uk/cern/cn50_intro.asp Study guide Remember that the expression for de Broglie wavelength is true for any particle, but the expression for photon energy (E=hf) is derived from this using the relativistic energy of a massless particle - thus it cannot be applied to the energy of a particle with non-zero mass. Understand how to apply the Heisenberg Uncertainty Principle to a range of situations, and note that con ...

Syracuse, PHY 361

Excerpt: ... Phy 361 Modern Physics Fall 2005 Homework Assignment 5 Due 10/4/05 Announcement: The first midterm exam will be on Thursday, October 6. It will be on all the material covered so far in class, i.e., Chapters 2, 3 and 4 of Beiser and all handouts. T ...