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Mathematical Methods For Physicists [Hardback]

(Infn, Italy), (Enea, Italy), (Enea Research Center, Frascati, Italy), (Enea Research Center, Frascati, Italy & Univ Of Rome La Sapienza, Italy)
  • Formāts: Hardback, 480 pages
  • Izdošanas datums: 04-Oct-2019
  • Izdevniecība: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9811201579
  • ISBN-13: 9789811201578
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  • Cena: 158,75 €
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Mathematical Methods For PhysicistsPalielināt
  • Formāts: Hardback, 480 pages
  • Izdošanas datums: 04-Oct-2019
  • Izdevniecība: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9811201579
  • ISBN-13: 9789811201578
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9789811201578.html
Keywords:
The book covers different aspects of mathematical methods for Physics. It is designed for graduate courses but a part of it can also be used by undergraduate students. The leitmotiv of the book is the search for a common mathematical framework for a wide class of apparently disparate physical phenomena. An important role, within this respect, is provided by a nonconventional formulation of special functions and polynomials. The proposed methods simplify the understanding of the relevant technicalities and yield a unifying view to their applications in Physics as well as other branches of science.The chapters are not organized through the mathematical study of specific problems in Physics, rather they are suggested by the formalism itself. For example, it is shown how the matrix formalism is useful to treat ray Optics, atomic systems evolution, QED, QCD and Feynman diagrams. The methods presented here are simple but rigorous. They allow a fairly substantive tool of analysis for a variety of topics and are useful for beginners as well as the more experienced researchers.
Abstract xiii
1 Matrices, Exponential Operators and Physical Applications 1(62)
1.1 Introduction
1(5)
1.2 Pauli Matrices
6(6)
1.3 Applications of 2 x 2 Matrices
12(17)
1.3.1 Classical Optics: Ray Beam Propagation and ABCD Law
12(7)
1.3.2 Quantum Mechanics
19(3)
1.3.3 Particle Physics: Kaon Mixing
22(7)
1.4 Cabibbo Angle and See-Saw Mechanism
29(4)
1.5 Gell-Mann and Pauli Matrices
33(10)
1.5.1 Spin Composition
33(3)
1.5.2 Gell-Mann Matrices
36(2)
1.5.3 Flavors and Spin
38(3)
1.5.4 Color and QCD
41(2)
1.6 Concluding Remarks
43(16)
1.6.1 Vector Differential Equations and Matrices
44(3)
1.6.2 Matrices, Vector Equations and Rotations
47(3)
1.6.3 Cabibbo-Kobayashi-Maskawa Matrix
50(1)
1.6.4 Frenet-Serret Equations
51(1)
1.6.5 Matrix, Rotations and Euler Angles
52(1)
1.6.6 4-Vectors and Lorentz Transformations
53(2)
1.6.7 Dirac Matrices
55(4)
Bibliography
59(4)
2 Ordinary and Partial Differential Equations, Evolution Operator Method and Applications 63(38)
2.1 Ordinary Differential Equations, Matrices and Exponential Operators
63(3)
2.2 Partial Differential Equations and Exponential Operators, I
66(6)
2.3 Partial Differential Equations and Exponential Operators, II
72(1)
2.4 Operator Ordering
73(6)
2.5 Schrodinger Equation and Paraxial Wave Equation of Classical Optics
79(5)
2.6 Examples of Fokker-Planck, Schrodinger and Liouville Equations
84(4)
2.7 Concluding Remarks
88(7)
Bibliography
95(6)
3 Hermite Polynomials and Applications 101(34)
3.1 Introduction
101(3)
3.2 Hermite Polynomials Generating Function
104(5)
3.2.1 Introducing the Generating Function
104(2)
3.2.2 Generating Function Applications
106(3)
3.3 Hermite Polynomials as an Orthogonal Basis
109(4)
3.4 Hermite Polynomials in Quantum Mechanics: Creation and Annihilation Operators
113(4)
3.5 Quantum Mechanics Applications
117(4)
3.6 Coherent or Quasi-Classical States of Harmonic Oscillators
121(6)
3.7 Jaynes-Cummings Model
127(2)
3.8 Classical Optics and Hermite Polynomials
129(3)
Bibliography
132(3)
4 Laguerre Polynomials, Integral Operators and Applications 135(32)
4.1 Introduction
135(5)
4.2 Laguerre Polynomials Generating Function
140(1)
4.3 Orthogonality Properties of Laguerre Polynomials
141(3)
4.4 Bessel Functions
144(4)
4.5 Associated Laguerre Polynomials
148(3)
4.6 Legendre Polynomials
151(2)
4.7 Miscellaneous Applications and Comments
153(5)
4.8 Appel Polynomials and Final Comments
158(5)
Bibliography
163(4)
5 Exercises and Complements I 167(50)
5.1 Pauli and Jones Matrices and Mueller Calculus
167(7)
5.2 Magnetic Lenses and Matrix Description
174(8)
5.3 Miscellanea on the Matrix Formalism and Solution of Evolution Problems
182(4)
5.3.1 Matrices and Quaternions
182(1)
5.3.2 Matrix Solution of Evolution Problems
183(3)
5.4 Lorentz Transformation
186(3)
5.5 Hyperbolic Trigonometry and Special Relativity
189(5)
5.6 A Touch on Elliptic Functions
194(13)
5.7 Concluding Comments
207(5)
Bibliography
212(5)
6 Exercises and Complements II 217(56)
6.1 Ordinary Differential Equations and Matrices
217(13)
6.2 Crofton-Glaisher Identities and Heat Type Equations
230(5)
6.3 Gamma Function and Definite Integrals
235(9)
6.4 Complex Variable Method and Evaluation of Integrals
244(6)
6.5 Fourier Transform
250(9)
6.6 Fourier Transform and the Solution of Differential Equations
259(3)
6.7 Fourier-Type Transforms
262(5)
Bibliography
267(6)
7 Exercises and Complements III 273(46)
7.1 Second Solution of Hermite Equation
273(2)
7.2 Higher Orders Hermite Polynomials
275(5)
7.3 Multi-Index Hermite Polynomials
280(4)
7.4 Creation-Annihilation Operators Algebra and Physical Applications
284(6)
7.5 Eisenstein Integers
290(5)
7.6 Harmonic Oscillator Hamiltonian Formal Aspects and Further Miscellaneous Considerations
295(3)
7.7 Time-Dependent Hamiltonians
298(1)
7.8 Dyson Series
299(8)
7.8.1 Beyond the Dyson Expansion
303(4)
7.9 Special Polynomials and Perturbation Theory
307(4)
Bibliography
311(8)
8 Exercises and Complements IV 319(36)
8.1 Sturm-Liouville Problem
319(5)
8.2 Green's Functions
324(2)
8.3 Laguerre Polynomials, Associated Operators and PDE
326(5)
8.4 Appel Polynomials, Associated Operators and Partial Differential Equations
331(6)
8.5 Riemann Function
337(5)
8.6 Bessel Special Functions
342(9)
Bibliography
351(4)
9 Special Functions, Umbral Methods and Applications 355(56)
9.1 Introduction to Umbral Methods and Relevant Applications
355(7)
9.2 Further Comments on Umbral Methods, Infinite Integrals and Borel Transform
362(6)
9.3 Borel Transform and Applications
368(10)
9.3.1 Borel - Pade
371(7)
9.4 Umbral Formalism and Laguerre Polynomials
378(2)
9.5 Umbral Formalism and Hermite Polynomials
380(2)
9.6 Umbral Formalism and Operator Ordering
382(4)
9.7 Mittag-Leffler Function and Fractional Calculus Application
386(6)
9.8 Formalism of Negative Derivative and Definite Integrals
392(2)
9.9 Umbral Formalism, Dual Numbers and Super-Gaussian Beam Transport
394(9)
Bibliography
403(8)
10 A Glimpse into the Math of the Feynman Diagrams 411(49)
10.1 Introduction Non Relativistic Scattering Theory and Lippman-Schwinger Equation
411(6)
10.2 Fermi Golden Rule
417(6)
10.2.1 Fermi Golden Rule Application
421(2)
10.3 Feynman Diagrams: Introductory Rules
423(4)
10.4 Virtual Particles and Propagators
427(3)
10.5 Space and Time like Feynman Diagrams
430(1)
10.6 Dirac Gamma Matrices
431(8)
10.7 Mathematics of the Dirac Equation
439(6)
10.8 A Touch on Quantum Electrodynamics
445(5)
10.9 Formal Point of View to the Dimensions and Units in Physics
450(10)
Bibliography 460(3)
Index 463