Waves and Optics

Description

This book covers all aspects of waves and optics ranging from one dimensional waves in a vibrating string, two dimensional waves in a vibrating membrane, both of which are transverse, three dimensional electromagnetic waves generated by radiating antennas and longitudinal sound/pressure waves in an air column. Note: T&F does not sell or distribute the Hardback in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka. Cover Half Title Title Page Copyright Page Table of Contents Chapter 1: The wave equation with examples from mechanics, optics, electromagnetism and quantum mechanics 1.1 The Definition of a propagating wave in one, two and three dimensions 1.2 Standing waves in one, two and three dimensions 1.3 The polarization of a wave 1.4 The wave equation in one, two and three dimensions 1.5 The polarization of a wave revisited 1.6 Basics of fluid dynamics 1.7 Waves in a fluid–derivation from first principles 1.8 Longitudinal sound/pressure waves in a tube 1.9 The difference between transverse and longitudinal waves in terms of wave polarization 1.10 Maxwell’s equations and the wave equation for the electric and magnetic fields in free space 1.11 Solution to Maxwell’s equations in terms of retarded potentials satisfying the wave equation with source 1.12 The principle of superposition 1.13 Diffraction and interference of waves 1.14 Green’s function for wave equation with sources–Fraunhoffer and Fresnel’s diffraction 1.15 The basic Eikonal equation of geometric optics 1.16 Describing the trajectory of light in a medium having spatially varying refractive index 1.17 Propagation of light in anisotropic, inhomogeneous and time varying medium 1.18 The Schrodinger wave equation in quantum mechanics 1.19 The effect of noise on the Schrodinger wave equation–Open systems, ie, coupling of the system to the bath environment 1.20 Wave equation with random non-uniform refractive index 1.21 The relationship between the wave equation and the Helmholtz equation for waves of given frequency 1.22 Waves in a confined region 1.23 Schrodinger’s wave equation for mixed states in the position kernel domain Chapter 2: Waves in general relativity, quantum gravity, plasma physics and quantum stochastics 2.1 Gravitational waves 2.2 Quantum gravity, the canonical ADM formalism-Schrodinger’s equation for the wave function of the space-time metric. 2.3 Plasma waves 2.4 Evans-Hudson diffusion as a quantum mechanical generalization of the wave equation with noise 2.5 Waves in an expanding universe–Newtonian theory of small fluctuations and general relativistic theory of small fluctuations 2.6 EMwaves in a curved space-time geometry with inhomogeneous permittivitypermeability tensor 2.7 Quantum Optics. Here, the photon field is a quantum electromagnetic field expressible as a superposition of annihilation and creation operators of the photon field with the coefficients of the linear combination being positions of time and space 2.8 Quantum optics, notion of a generalized measurement, state collapse after quantum measurement, recovery of states passed through a noisy quantum system, the Knill-Laflamme theorem Stinspring’s representation of noisy quantum systems, Information, relative entropy, mutual information and Renyi entropy of quantum systems. Transmission of information over quantum system. The relevance of all this to the wave mechanics of Schrodinger 2.9 Controlling the quantum em field produced by electrons and positrons by using a classical em field-An application of Dirac’s relativistic wave equation 2.10 Calculating the path of a light ray in a static gravitational field 2.11 A study of thermal emission by blackholes via Hawking radiation, quantum mechanics of fields in the vicinity of a blackhole and the interactio of electrons, positrons, photons and gravitons with an external noisy bath with application to the design of very large size quantum gates Chapter 3: Analysis of waves in engineering and optical systems, in biological systems, classical and in quantum blackhole physics 3.1 Wave digital filter design 3.2 Large deviation principle in wave-motion 3.3 Some more problems in Schrodinger-wave mechanics and Heisenbergmatrix mechanics with relevance to quantum information theory 3.4 Questions in optimization techniques 3.5 Quantum antennas via the Schrodinger wave equation 3.6 Linear algebra for quantum information theory 3.7 Transmission lines and waveguides–Questions 3.8 Some more matrix inequalities related to quantum information theory 3.9 Fresnel and Fraunhoffer diffraction 3.10 Surface tension and wave propagation 3.11 Klein-Gordon equation in the Schwarzchild space-time with a radialtime independent electromagnetic field and its application to computing the Hawking temperature at which massless/massive particles are emitted from a blackhole 3.12 Quantum Belavkin filtering versus classical Kushner-Kallianpur filtering–A comparison 3.13 Remark on quantum Belavkin filtering for estimating the state of a quantum vibrating string 3.14 Elementary problems in robotics based on damped simple harmonicmotion 3.15 Approximate solution to the Dirac equation in curved space-time 3.16 Some applications of quantum gate design using physical systems 3.17 Convergence of perturbation series for nonlinear differential equations 3.18 Poiseulle’s law and generalized Poiseulle’s law for flow through a pipe 3.19 Measurement of refractive index 3.20 Modes of a vibrating string with applications to particle physics 3.21 Hidden Markov Models for estimating the amplitude, frequency and phase of a sinusoidal signal making transitions 3.22 The energy-momentum tensor of the Dirac field in a background curved space-time metric 3.23 Remark on Noether’s theorem on conserved currents 3.24 Energy-momentum tensor using the tetrad formalism 3.25 Analysis of gravitational waves produced by a finite system of point particles–A perturbation theoretic approach 3.26 Heat equation and its solution in Rn, relationship between heat and wave equations, nonlinear heat equations arising as the scaling limit of the simple exclusion process 3.27 Study of wave motion of the boundary of single cellular micro-organsims by giving them external stimulus and observing the wave like motion of their boundary walls as well as wave-like fluctuations of the velocity field of the cytoplasmic fluid within them 3.28 Snell’s laws of reflection and refraction on surfaces separating two uniform media 3.29 Spinor form of some equations of mathematical physics: Roger Penrose’s theory 3.30 Prisms, mirrors and lenses, the general theory 3.31 A brief summary of the book Chapter 4: Probability Theory and Statistics required for random wave motion analysis 4.1 Summary of contents 4.2 Probability spaces and measure theoretic theorems on probability spaces 4.3 Basic facts about quantum probability 4.4 Some basic classical and quantum stochastic processes 4.5 Some applications of classical probability to engineering systems 4.6 Quantum stochastic differential equations 4.7 Some practical applications of quantum probability 4.8 Casting the HP equation in functional derivative form Chapter 5: An introduction to probability and random processes in circuit and field theory from a pedagogical viewpoint 5.1 Circuit theory concepts from field theory concepts 5.2 Graph theoretic analysis of large linear circuits based on KCL and KVL 5.3 Two port network theory 5.4 Diode and capacitance circuit models 5.5 Classical device physics 5.6 Device physics using quantum mechanics and quantum electrodynamics 5.7 Band theory of a semiconductor by solving Schrodinger’s equation 5.8 Quantum electrodynamics and quantum field theory 5.9 Analyzing random Gaussian and non-Gaussian noise in circuits using higher order correlations and spectra 5.10 Noise in nonlinear transistor circuits 5.11 Digital electronics 5.12 Techniques for analyzing transmission lines 5.13 Brownian motion, Poisson processes and stochastic differential equations in circuit theory 5.14 Classical and quantum random processes in circuit theory 5.15 Simulation of nonlinear ode’s and pde’s in circuit theory and electromagnetics 5.16 Derivation of medium properties from basic physical principles involving motion of individual electrons and magnetic moments in external fields 5.17 Partial differential equation methods for analyzing waveguides 5.18 Curvilinear coordinate systems and variational methods in engineering electromagnetics 5.19 Perturbation theoretic methods in solving electromagnetics problems 5.20 Numerical methods in antenna, waveguide and cavity resonator theory 5.21 Large deviation theory applied to engineering systems 5.22 Robotics based on nonlinear differential equations 5.23 Quantization of robot motion 5.24 Filtering and control of engineering systems 5.25 Quantum many body systems applied to Fermi operator fields and superconductivity 5.26 Lie group theory in image processing 5.27 Lie group based robotics 5.28 Levy process models for jerk noise in robotic systems 5.29 Digital systems, classical and quantum gates, design of counters using shift registers and flip-flops 5.30 HMM and some of its applications 5.31 Quantum Image Processing 5.32 Introduce the design aspects of some gadgets through mini-projects some examples 5.33 A simple way to introduce quantum electrodynamics 5.34 How to teach the theory of non-Abelian gauge theories as non-commutative generalizations of electromagnetism 5.35 How to introduce astronomy and cosmology to undergraduates 5.36 Quantum image processing revisited 5.37 The EKF for arbitrary Markov processes with Gaussian measurementnoise 5.38 Quantum scattering theory applied to quantum gate design 5.39 Superconductivity for two species and interpretation of the gap function 5.40 Introductory quantum information theory 5.41 Quantum image processing 5.42 Lie group-Lie algebra approach to robot dynamics with two 3 − D links, each described by three Euler angles and an overall translational vector a(t) ∈ R3 5.43 Linear algebra and operator theory Chapter 6: Applications of Lie groups and Lie algebras, filtering, field quantization, Numerical methods for quantum mechanical problems 6.1 Quantum random walk 6.2 Lie group-Lie algebra theoretic coordinate free formulation of the equations of motion of a robot with N 3-D links with the orientation of each link described by an arbitrary element of SO(3) and taking in addition into account a translation of the base pivot of the first link 6.3 Numerical methods for computing transition probabilities for photons, gravitons, Klein-Gordon Bosons, Dirac Fermions and non-Abelian matter and gauge particles from inside the critical radius to outside of a Schwarzchild blackhole with quantum gate design applications 6.4 Numerical methods for designing quantum gates based on quantum scattering theory for a Schrodinger projectile interacting with a potential 6.5 Quantization of a robot in the Lie-group domain when the robot has N 3-D links 6.6 Lie group formulation of the single 3-D robot link in the presence ofgravitation and external torque 6.7 Quantum antennas based on non-Abelian matter and gauge fields 6.8 The electroweak theory 6.9 Wavelet based system parameter estimation 6.10 Applying the EKF to nonlinear circuits involving diodes and transistors 6.11 An introduction to classical and quantum error detecting and correcting codes 6.12 Orthogonal Latin squares and coding theory 6.13 Cyclic codes 6.14 Yang-Mills field quantization methods 6.15 The Ginzburg-Landau model for superconductivity 6.16 Teaching the basics of classical mechanics to school students and first year undergraduates 6.17 Teaching Linear algebra and functional analysis to post-graduate students of signal processing 6.18 Variants of the Kalman filter 6.19 The Cq-coding theorem: Proof based on Quantum Renyi entropy and Shannon’s random coding argument 6.20 Manual for the Digital Signal Processing and Statistical Signal Processing Laboratory 6.21 MATLAB problems on root space decomposition of a Lie algebra 6.22 Cartan’s criterion for semisimplicity of a Lie algebra 6.23 Problems in linear algebra 6.24 Problems in non-linear filtering theory 6.25 Spectral theorem for bounded self-adjoint operators in a Hilbert space–basic steps 6.26 Motion of rigid bodies in electromagnetic fields 6.27 Large deviation theory with engineering applications 6.28 Lectures in linear algebra for signal processing applications 6.29 On the improvement of the signal quality in telephone lines 6.30 Quantum Coulomb scattering 6.31 Tutorial problems in electromagnetic field theory 6.32 Lecture plan for electromagnetic field theory EC-C09 6.33 A digression into infinite dimensional vector spaces 6.34 Continuation of finite dimensional vector spaces 6.35 The general relativistic Maxwell equations in a resonator 6.36 Mackey’s theory on the construction of the basic observables in the quantum theory from projective unitary representations of the Galilean group 6.37 Hamiltonian density of the electromagnetic field in curved space-time in terms of position and momentum fields 6.38 Coulomb scattering 6.39 Electromagnetic waves in the Schwarzchild metric 6.40 Tutorial problems in electromagnetic field theory 6.41 The gravitational n-body problem in general relativity: an approximate treatment 6.42 Lecture plan for ”Linear Algebra in Signal Processing”-SP-C01 6.43 Continuation of finite dimensional vector spaces 6.44 Cartan’s equations of structure 6.45 Proof of the Riesz representation theorem 6.46 Quantum image processing 6.47 Inclusion of the Goldstone boson field in the gauge field after symmetry breaking 6.48 Some problems in linear algebra 6.49 Gravitational N-body problem in general relativity 6.50 Multipole radiation fields in the Maxwell theory 6.51 How Dirac brackets are used to take care of constraints in Lagrangian and Hamiltonian mechanics 6.52 Deep learning of speech models 6.53 Some problems on linearization (for the course Linear algebra in signal processing) 6.54 Research project proposal for simulating quantum gates of large sizes using quantized ridge waveguide electromagnetic field interacting with quantum dots and also for estimating medium properties on the Angstrom scale 6.55 Design of a differentiator using series connection of short circuitedtransmission line elements 6.56 Design of quantum gates by interaction of a quantum em field with gravity 6.57 Scattering theory in the interaction picture for time dependent interations 6.58 Chapterwise report on Jaspal Khinda’s Ph.D thesis 6.59 Training a DNN with stochastic inputs with analysis of the robustness against input process and weight matrix fluctuations 6.60 Quantum Boltzmann equation 6.61 List of Ph.D scholars supervised by Harish Parthasarathy with a brief summary of their theses 6.62 The problem of determining the surface current density induced on an antenna surface placed in a nonlinear inhomogeneous and anisotropic medium taking gravitational effects into account