Introduction to Quantum Mechanics 2Nd Edition Pdf, Epub, Ebook
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Chapter 5 Semiconductor Laser
Chapter 5 Semiconductor Laser _____________________________________________ 5.0 Introduction Laser is an acronym for light amplification by stimulated emission of radiation. Albert Einstein in 1917 showed that the process of stimulated emission must exist but it was not until 1960 that TH Maiman first achieved laser at optical frequency in solid state ruby. Semiconductor laser is similar to the solid state laser like the ruby laser and helium-neon gas laser. The emitted radiation is highly monochromatic and produces a highly directional beam of light. However, the semiconductor laser differs from other lasers because it is small in 0.1mm long and easily modulated at high frequency simply by modulating the biasing current. Because of its uniqueness, semiconductor laser is one of the most important light sources for optical-fiber communication. It can be used in many other applications like scientific research, communication, holography, medicine, military, optical video recording, optical reading, high speed laser printing etc. The analysis of physics of laser is quite difficult and we summarize with the simplified version here. The application of laser although with a slow start in the 1960s but now very often new applications are found such as those mentioned earlier in the text. 5.1 Emission and Absorption of Radiation As mentioned in earlier Chapter, when an electron in an atom undergoes transition between two energy states or levels, it either absorbs or emits photon. When the electron transits from lower energy level to higher energy level, it absorbs photon. When an electron transits from higher energy level to lower energy level, it releases photon. -
Schrödinger Equation)
Lecture 37 (Schrödinger Equation) Physics 2310-01 Spring 2020 Douglas Fields Reduced Mass • OK, so the Bohr model of the atom gives energy levels: • But, this has one problem – it was developed assuming the acceleration of the electron was given as an object revolving around a fixed point. • In fact, the proton is also free to move. • The acceleration of the electron must then take this into account. • Since we know from Newton’s third law that: • If we want to relate the real acceleration of the electron to the force on the electron, we have to take into account the motion of the proton too. Reduced Mass • So, the relative acceleration of the electron to the proton is just: • Then, the force relation becomes: • And the energy levels become: Reduced Mass • The reduced mass is close to the electron mass, but the 0.0054% difference is measurable in hydrogen and important in the energy levels of muonium (a hydrogen atom with a muon instead of an electron) since the muon mass is 200 times heavier than the electron. • Or, in general: Hydrogen-like atoms • For single electron atoms with more than one proton in the nucleus, we can use the Bohr energy levels with a minor change: e4 → Z2e4. • For instance, for He+ , Uncertainty Revisited • Let’s go back to the wave function for a travelling plane wave: • Notice that we derived an uncertainty relationship between k and x that ended being an uncertainty relation between p and x (since p=ћk): Uncertainty Revisited • Well it turns out that the same relation holds for ω and t, and therefore for E and t: • We see this playing an important role in the lifetime of excited states. -
Auger Recombination in Quantum Well Laser with Participation of Electrons in Waveguide Region
ARuegv.e Ar drev.c Momatbeinr.a Sticoi.n 5 in7 q(2u0a1n8tu) m19 w3-e1ll9 la8ser with participation of electrons in waveguide region 193 AUGER RECOMBINATION IN QUANTUM WELL LASER WITH PARTICIPATION OF ELECTRONS IN WAVEGUIDE REGION A.A. Karpova1,2, D.M. Samosvat2, A.G. Zegrya2, G.G. Zegrya1,2 and V.E. Bugrov1 1Saint Petersburg National Research University of Information Technologies, Mechanics and Optics, Kronverksky Pr. 49, St. Petersburg, 197101 Russia 2Ioffe Institute, Politekhnicheskaya 26, St. Petersburg, 194021 Russia Received: May 07, 2018 Abstract. A new mechanism of nonradiative recombination of nonequilibrium carriers in semiconductor quantum wells is suggested and discussed. For a studied Auger recombination process the energy of localized electron-hole pair is transferred to barrier carriers due to Coulomb interaction. The analysis of the rate and the coefficient of this process is carried out. It is shown, that there exists two processes of thresholdless and quasithreshold types, and thresholdless one is dominant. The coefficient of studied process is a non-monotonous function of quantum well width having maximum in region of narrow quantum wells. Comparison of this process with CHCC process shows that these two processes of nonradiative recombination are competing in narrow quantum wells, but prevail at different quantum well widths. 1. INTRODUCTION nonequilibrium carriers is still located in the waveguide region. Nowadays an actual research field of semiconduc- In present work a new loss channel in InGaAsP/ tor optoelectronics is InGaAsP/InP multiple quan- InP MQW lasers is under consideration. It affects tum well (MQW) lasers, because their lasing wave- significantly the threshold characteristics of laser length is 1.3 – 1.55 micrometers and coincides with and leads to generation failure at high excitation transparency windows of optical fiber [1-5]. -
Modern Physics: Problem Set #5
Physics 320 Fall (12) 2017 Modern Physics: Problem Set #5 The Bohr Model ("This is all nonsense", von Laue on Bohr's model; "It is one of the greatest discoveries", Einstein on the same). 2 4 mek e 1 ⎛ 1 ⎞ hc L = mvr = n! ; E n = – 2 2 ≈ –13.6eV⎜ 2 ⎟ ; λn →m = 2! n ⎝ n ⎠ | E m – E n | Notes: Exam 1 is next Friday (9/29). This exam will cover material in chapters 2 through 4. The exam€ is closed book, closed notes but you may bring in one-half of an 8.5x11" sheet of paper with handwritten notes€ and equations. € Due: Friday Sept. 29 by 6 pm Reading assignment: for Monday, 5.1-5.4 (Wave function for matter & 1D-Schrodinger equation) for Wednesday, 5.5, 5.8 (Particle in a box & Expectation values) Problem assignment: Chapter 4 Problems: 54. Bohr model for hydrogen spectrum (identify the region of the spectrum for each λ) 57. Electron speed in the Bohr model for hydrogen [Result: ke 2 /n!] A1. Rotational Spectra: The figure shows a diatomic molecule with bond- length d rotating about its center of mass. According to quantum theory, the d m ! ! ! € angular momentum ( ) of this system is restricted to a discrete set L = r × p m of values (including zero). Using the Bohr quantization condition (L=n!), determine the following: a) The allowed€ rotational energies of the molecule. [Result: n 2!2 /md 2 ] b) The wavelength of the photon needed to excite the molecule from the n to the n+1 rotational state. -
Bohr Model of Hydrogen
Chapter 3 Bohr model of hydrogen Figure 3.1: Democritus The atomic theory of matter has a long history, in some ways all the way back to the ancient Greeks (Democritus - ca. 400 BCE - suggested that all things are composed of indivisible \atoms"). From what we can observe, atoms have certain properties and behaviors, which can be summarized as follows: Atoms are small, with diameters on the order of 0:1 nm. Atoms are stable, they do not spontaneously break apart into smaller pieces or collapse. Atoms contain negatively charged electrons, but are electrically neutral. Atoms emit and absorb electromagnetic radiation. Any successful model of atoms must be capable of describing these observed properties. 1 (a) Isaac Newton (b) Joseph von Fraunhofer (c) Gustav Robert Kirch- hoff 3.1 Atomic spectra Even though the spectral nature of light is present in a rainbow, it was not until 1666 that Isaac Newton showed that white light from the sun is com- posed of a continuum of colors (frequencies). Newton introduced the term \spectrum" to describe this phenomenon. His method to measure the spec- trum of light consisted of a small aperture to define a point source of light, a lens to collimate this into a beam of light, a glass spectrum to disperse the colors and a screen on which to observe the resulting spectrum. This is indeed quite close to a modern spectrometer! Newton's analysis was the beginning of the science of spectroscopy (the study of the frequency distri- bution of light from different sources). The first observation of the discrete nature of emission and absorption from atomic systems was made by Joseph Fraunhofer in 1814. -
Bohr's 1913 Molecular Model Revisited
Bohr’s 1913 molecular model revisited Anatoly A. Svidzinsky*†‡, Marlan O. Scully*†§, and Dudley R. Herschbach¶ *Departments of Chemistry and Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544; †Departments of Physics and Chemical and Electrical Engineering, Texas A&M University, College Station, TX 77843-4242; §Max-Planck-Institut fu¨r Quantenoptik, D-85748 Garching, Germany; and ¶Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138 Contributed by Marlan O. Scully, July 10, 2005 It is generally believed that the old quantum theory, as presented by Niels Bohr in 1913, fails when applied to few electron systems, such as the H2 molecule. Here, we find previously undescribed solutions within the Bohr theory that describe the potential energy curve for the lowest singlet and triplet states of H2 about as well as the early wave mechanical treatment of Heitler and London. We also develop an interpolation scheme that substantially improves the agreement with the exact ground-state potential curve of H2 and provides a good description of more complicated molecules such as LiH, Li2, BeH, and He2. Bohr model ͉ chemical bond ͉ molecules he Bohr model (1–3) for a one-electron atom played a major Thistorical role and still offers pedagogical appeal. However, when applied to the simple H2 molecule, the ‘‘old quantum theory’’ proved unsatisfactory (4, 5). Here we show that a simple extension of the original Bohr model describes the potential energy curves E(R) for the lowest singlet and triplet states about Fig. 1. Molecular configurations as sketched by Niels Bohr; [from an unpub- as well as the first wave mechanical treatment by Heitler and lished manuscript (7), intended as an appendix to his 1913 papers]. -
Bohr's Model and Physics of the Atom
CHAPTER 43 BOHR'S MODEL AND PHYSICS OF THE ATOM 43.1 EARLY ATOMIC MODELS Lenard's Suggestion Lenard had noted that cathode rays could pass The idea that all matter is made of very small through materials of small thickness almost indivisible particles is very old. It has taken a long undeviated. If the atoms were solid spheres, most of time, intelligent reasoning and classic experiments to the electrons in the cathode rays would hit them and cover the journey from this idea to the present day would not be able to go ahead in the forward direction. atomic models. Lenard, therefore, suggested in 1903 that the atom We can start our discussion with the mention of must have a lot of empty space in it. He proposed that English scientist Robert Boyle (1627-1691) who the atom is made of electrons and similar tiny particles studied the expansion and compression of air. The fact carrying positive charge. But then, the question was, that air can be compressed or expanded, tells that air why on heating a metal, these tiny positively charged is made of tiny particles with lot of empty space particles were not ejected ? between the particles. When air is compressed, these 1 Rutherford's Model of the Atom particles get closer to each other, reducing the empty space. We mention Robert Boyle here, because, with Thomson's model and Lenard's model, both had him atomism entered a new phase, from mere certain advantages and disadvantages. Thomson's reasoning to experimental observations. The smallest model made the positive charge immovable by unit of an element, which carries all the properties of assuming it-to be spread over the total volume of the the element is called an atom. -
Ab Initio Calculation of Energy Levels for Phosphorus Donors in Silicon
Ab initio calculation of energy levels for phosphorus donors in silicon J. S. Smith,1 A. Budi,2 M. C. Per,3 N. Vogt,1 D. W. Drumm,1, 4 L. C. L. Hollenberg,5 J. H. Cole,1 and S. P. Russo1 1Chemical and Quantum Physics, School of Science, RMIT University, Melbourne VIC 3001, Australia 2Materials Chemistry, Nano-Science Center, Department of Chemistry, University of Copenhagen, Universitetsparken 5, 2100 København Ø, Denmark 3Data 61 CSIRO, Door 34 Goods Shed, Village Street, Docklands VIC 3008, Australia 4Australian Research Council Centre of Excellence for Nanoscale BioPhotonics, School of Science, RMIT University, Melbourne, VIC 3001, Australia 5Centre for Quantum Computation and Communication Technology, School of Physics, The University of Melbourne, Parkville, 3010 Victoria, Australia The s manifold energy levels for phosphorus donors in silicon are important input parameters for the design and modelling of electronic devices on the nanoscale. In this paper we calculate these energy levels from first principles using density functional theory. The wavefunction of the donor electron's ground state is found to have a form that is similar to an atomic s orbital, with an effective Bohr radius of 1.8 nm. The corresponding binding energy of this state is found to be 41 meV, which is in good agreement with the currently accepted value of 45.59 meV. We also calculate the energies of the excited 1s(T2) and 1s(E) states, finding them to be 32 and 31 meV respectively. These results constitute the first ab initio confirmation of the s manifold energy levels for phosphorus donors in silicon. -
Niels Bohr and the Atomic Structure
GENERAL ¨ ARTICLE Niels Bohr and the Atomic Structure M Durga Prasad Niels Bohr developed his model of the atomic structure in 1913 that succeeded in explaining the spectral features of hydrogen atom. In the process, he incorporated some non-classical features such as discrete energy levels for the bound electrons, and quantization of their angular momenta. Introduction MDurgaPrasadisa Professor of Chemistry An atom consists of two interacting subsystems. The first sub- at the University of system is the atomic nucleus, consisting of Z protons and A–Z Hyderabad. His research neutrons, where Z and A are the atomic number and atomic weight interests lie in theoretical respectively, of the concerned atom. The electrons that are part of chemistry. the second subsystem occupy (to zeroth order approximation) discrete energy levels, called the orbitals, according to the Aufbau principle with the restriction that no more than two electrons occupy a given orbital. Such paired electrons must have their spins in opposite direction (Pauli’s exclusion principle). The two subsystems interact through Coulomb attraction that binds the electrons to the nucleus. The nucleons in turn are trapped in the nucleus due to strong interactions. The two forces operate on significantly different scales of length and energy. Consequently, there is a clear-cut demarcation between the nuclear processes such as radioactivity or fission, and atomic processes involving the electrons such as optical spectroscopy or chemical reactivity. This picture of the atom was developed in the period between 1890 and 1928 (see the timeline in Box 1). One of the major figures in this development was Niels Bohr, who introduced most of the terminology that is still in use. -
Module P11.3 Schrödinger's Model of the Hydrogen Atom
FLEXIBLE LEARNING APPROACH TO PHYSICS Module P11.3 Schrödinger’s model of the hydrogen atom 1 Opening items 3.4 Ionization and degeneracy 1.1 Module introduction 3.5 Comparison of the Bohr and the Schrödinger 1.2 Fast track questions models of the hydrogen atom 1.3 Ready to study? 3.6 The classical limit 2 The early quantum models for hydrogen 4 Closing items 2.1 Review of the Bohr model 4.1 Module summary 2.2 The wave-like properties of the electron 4.2 Achievements 3 The Schrödinger model for hydrogen 4.3 Exit test 3.1 The potential energy function and the Exit module Schrödinger equation 3.2 Qualitative solutions for wavefunctions1 —1the quantum numbers 3.3 Qualitative solutions of the Schrödinger equation1—1the electron distribution patterns FLAP P11.3 Schrödinger’s model of the hydrogen atom COPYRIGHT © 1998 THE OPEN UNIVERSITY S570 V1.1 1 Opening items 1.1 Module introduction The hydrogen atom is the simplest atom. It has only one electron and the nucleus is a proton. It is therefore not surprising that it has been the test-bed for new theories. In this module, we will look at the attempts that have been made to understand the structure of the hydrogen atom1—1a structure that leads to a typical line spectrum. Nineteenth century physicists, starting with Balmer, had found simple formulae that gave the wavelengths of the observed spectral lines from hydrogen. This was before the discovery of the electron, so no theory could be put forward to explain the simple formulae. -
Electronic and Photonic Quantum Devices
Electronic and Photonic Quantum Devices Erik Forsberg Stockholm 2003 Doctoral Dissertation Royal Institute of Technology Department of Microelectronics and Information Technology Akademisk avhandling som med tillstºandav Kungl Tekniska HÄogskolan framlÄag- ges till offentlig granskning fÄoravlÄaggandeav teknisk doktorsexamen tisdagen den 4 mars 2003 kl 10.00 i sal C2, Electrum Kungl Tekniska HÄogskolan, IsafjordsvÄagen 22, Kista. ISBN 91-7283-446-3 TRITA-MVT Report 2003:1 ISSN 0348-4467 ISRN KTH/MVT/FR{03/1{SE °c Erik Forsberg, March 2003 Printed by Universitetsservice AB, Stockholm 2003 Abstract In this thesis various subjects at the crossroads of quantum mechanics and device physics are treated, spanning from a fundamental study on quantum measurements to fabrication techniques of controlling gates for nanoelectronic components. Electron waveguide components, i.e. electronic components with a size such that the wave nature of the electron dominates the device characteristics, are treated both experimentally and theoretically. On the experimental side, evidence of par- tial ballistic transport at room-temperature has been found and devices controlled by in-plane Pt/GaAs gates have been fabricated exhibiting an order of magnitude improved gate-e±ciency as compared to an earlier gate-technology. On the the- oretical side, a novel numerical method for self-consistent simulations of electron waveguide devices has been developed. The method is unique as it incorporates an energy resolved charge density calculation allowing for e.g. calculations of electron waveguide devices to which a ¯nite bias is applied. The method has then been used in discussions on the influence of space-charge on gate-control of electron waveguide Y-branch switches. -
An Introduction to Quantum Field Theory Free Download
AN INTRODUCTION TO QUANTUM FIELD THEORY FREE DOWNLOAD Michael E. Peskin,Daniel V. Schroeder | 864 pages | 01 Oct 1995 | The Perseus Books Group | 9780201503975 | English | Boulder, CO, United States An Introduction to Quantum Field Theory Totem Books. Perhaps they are produced by the excitation of a crystal that characteristically absorbs a photon of a certain frequency and emits two photons of half the original frequency. The other orbitals have more complicated shapes see atomic orbitaland are denoted by the letters dfgetc. In QED, its full description makes essential use of short lived virtual particles. Nobel Foundation. Problems 5. For a better shopping experience, please upgrade now. Planck's law explains why: increasing the temperature of a body allows it to emit more energy overall, An Introduction to Quantum Field Theory means that a larger proportion of the energy is towards the violet end of the spectrum. Main article: Double- slit experiment. We need to add that in the Lagrangian. This was one of the best courses I have ever taken: Professor Larsen did an excellent job both lecturing and coming up with interesting problems to work on. Something that is quantizedlike the energy of Planck's harmonic oscillators, can only take specific values. The quantum state of the An Introduction to Quantum Field Theory is described An Introduction to Quantum Field Theory its wave function. Quantum technology links Matrix isolation Phase qubit Quantum dot cellular automaton display laser single-photon source solar cell Quantum well laser. Conversely, an electron that absorbs a photon gains energy, hence it jumps to an orbit that is farther from the nucleus.