Mathematics of Classical and Quantum Physics, Volumes 1-2This textbook is designed to complement graduate-level physics texts in classical mechanics, electricity, magnetism, and quantum mechanics. Organized around the central concept of a vector space, the book includes numerous physical applications in the body of the text as well as many problems of a physical nature. It is also one of the purposes of this book to introduce the physicist to the language and style of mathematics as well as the content of those particular subjects with contemporary relevance in physics. Chapters 1 and 2 are devoted to the mathematics of classical physics. Chapters 3, 4 and 5 — the backbone of the book — cover the theory of vector spaces. Chapter 6 covers analytic function theory. In chapters 7, 8, and 9 the authors take up several important techniques of theoretical physics — the Green's function method of solving differential and partial differential equations, and the theory of integral equations. Chapter 10 introduces the theory of groups. The authors have included a large selection of problems at the end of each chapter, some illustrating or extending mathematical points, others stressing physical application of techniques developed in the text. Essentially self-contained, the book assumes only the standard undergraduate preparation in physics and mathematics, i.e. intermediate mechanics, electricity and magnetism, introductory quantum mechanics, advanced calculus and differential equations. The text may be easily adapted for a one-semester course at the graduate or advanced undergraduate level. |
Contents
II | ix |
V | 1 |
VI | 2 |
VII | 3 |
VIII | 12 |
IX | 15 |
X | 17 |
XI | 31 |
LXI | 251 |
LXIII | 259 |
LXIV | 261 |
LXV | 275 |
LXVI | 303 |
LXIX | 310 |
LXX | 320 |
LXXI | 328 |
XII | 41 |
XV | 43 |
XVI | 47 |
XVII | 51 |
XVIII | 59 |
XIX | 63 |
XX | 70 |
XXI | 83 |
XXV | 87 |
XXVII | 90 |
XXVIII | 93 |
XXIX | 96 |
XXX | 98 |
XXXI | 100 |
XXXII | 107 |
XXXIII | 118 |
XXXIV | 128 |
XXXV | 140 |
XXXIX | 143 |
XL | 146 |
XLI | 149 |
XLII | 154 |
XLIII | 156 |
XLV | 162 |
XLVI | 169 |
XLVII | 173 |
XLVIII | 182 |
XLIX | 190 |
L | 196 |
LI | 210 |
LIV | 211 |
LV | 215 |
LVI | 222 |
LVII | 226 |
LVIII | 231 |
LIX | 237 |
LX | 244 |
LXXII | 333 |
LXXIII | 338 |
LXXIV | 347 |
LXXV | 356 |
LXXVI | 369 |
LXXVII | 386 |
LXXXI | 393 |
LXXXII | 399 |
LXXXIII | 409 |
LXXXIV | 418 |
LXXXV | 431 |
LXXXVI | 440 |
LXXXVII | 451 |
LXXXVIII | 467 |
XCII | 472 |
XCIII | 477 |
XCIV | 482 |
XCV | 494 |
XCVI | 501 |
XCVII | 516 |
CI | 529 |
CII | 539 |
CIII | 547 |
CIV | 553 |
CV | 561 |
CVI | 578 |
CX | 584 |
CXI | 590 |
CXII | 597 |
CXIII | 602 |
CXIV | 608 |
CXV | 620 |
CXVI | 631 |
CXVII | 647 |
CXVIII | 649 |
655 | |
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Mathematics of Classical and Quantum Physics Frederick W. Byron,Robert W. Fuller Limited preview - 2012 |
Common terms and phrases
a₁ analytic function assume b₁ basis boundary conditions C₂ coefficients completely continuous complex numbers components consider constant contour convergence coordinates corresponding defined definition denote derivative determined diagonal differential equation eigenfunctions eigenvalues eigenvectors elements example exists finite-dimensional follows Fourier transform G₁ given Green's function Hence Hermitian Hermitian operator Hilbert space inner product inner-product space integral equation interval invariant inverse irreducible representations kernel Legendre polynomials linear combination linear operator linear transformation linearly independent matrix multiplication norm Note obtain orthogonal physical polynomials potential problem proof prove quantum mechanics reader real axis result rotation satisfy scalar Section self-adjoint self-adjoint operator sequence set of functions singular solution solve spherical square-integrable subgroup symmetric tensor theorem theory tion unitary vanishes variable vector space write x₁ zero ду