Some Mathematical Methods of PhysicsThis well-rounded, thorough treatment for advanced undergraduates and graduate students introduces basic concepts of mathematical physics involved in the study of linear systems. The text emphasizes eigenvalues, eigenfunctions, and Green's functions. Prerequisites include differential equations and a first course in theoretical physics. The three-part presentation begins with an exploration of systems with a finite number of degrees of freedom (described by matrices). In part two, the concepts developed for discrete systems in previous chapters are extended to continuous systems. New concepts useful in the treatment of continuous systems are also introduced. The final part examines approximation methods — including perturbation theory, variational methods, and numerical methods — relevant to addressing most of the problems of nature that confront applied physicists. Two Appendixes include background and supplementary material. 1960 edition. |
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Recurrence Relations for the Spherical Harmonics Some Expansion Theorems Solution of the Wave Equation . 11.10 Heat Conduction in an Infinite Solid Chapter 12 12.1 12.2 12.3 12.4 12.5 Green's Functions Definition .
Recurrence Relations for the Spherical Harmonics Some Expansion Theorems Solution of the Wave Equation . 11.10 Heat Conduction in an Infinite Solid Chapter 12 12.1 12.2 12.3 12.4 12.5 Green's Functions Definition .
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Before entering into the main subject of this section, it is desirable to introduce a notation which enables one to write the required relations in concise and clear form. The new concept is the summation symbol 2. Let ,, i = 1, 2, ...
Before entering into the main subject of this section, it is desirable to introduce a notation which enables one to write the required relations in concise and clear form. The new concept is the summation symbol 2. Let ,, i = 1, 2, ...
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This matrix satisfies the relations Im = ml = m (1.33) It should be noted here that unless m is square, two distinct matrices I are involved in (1.33). The unit matrix I has the following form—all of (1.32) its elements along the main ...
This matrix satisfies the relations Im = ml = m (1.33) It should be noted here that unless m is square, two distinct matrices I are involved in (1.33). The unit matrix I has the following form—all of (1.32) its elements along the main ...
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That is Ii,- = 6,, (1.34) where the symbol 6,,- is the Kronecker delta symbol and is defined by the following relations 6,, = 1 6,, = 0 for 1' 7i j The importance of the Kronecker delta arises from (1.34) and from the corresponding ...
That is Ii,- = 6,, (1.34) where the symbol 6,,- is the Kronecker delta symbol and is defined by the following relations 6,, = 1 6,, = 0 for 1' 7i j The importance of the Kronecker delta arises from (1.34) and from the corresponding ...
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With this familiar symbolism, it will seem more plausible to consider functions of matrices,1 power series involving matrices, and similar relations than it would if special notations were used when handling matrices.
With this familiar symbolism, it will seem more plausible to consider functions of matrices,1 power series involving matrices, and similar relations than it would if special notations were used when handling matrices.
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applied approximate arbitrary base vectors basis Bessel function boundary conditions Chap chapter coefficients column commute complete consider constant continuous systems contour corresponding cylindrical functions defined definition denoted determinant diagonal diagonalizable differential equation Dirac notation domain eigen eigencolumns eigenfunctions eigenvalue equation eigenvector elements evaluate expansion find finite number first follows formula Fourier given Green’s function Hence Hermitian matrix Hermitian operator infinite integral Introduction inverse Laplacian linear operator linearly independent lowest eigenvalue matrix McGraw-Hill Book Company membrane method multiplication nonsingular normal normal matrix Note number of degrees obtained orthonormality conditions perturbation plane procedure QUANTUM MECHANICS relations representation result Ritz method satisfies satisfy scattering solve specified spherical spherical harmonics string Substitution theorem theory tion trial functions vanish variable vector space verified wave write written yields York zero
Información bibliográfica
| Título | Some Mathematical Methods of Physics Dover Books on Physics |
| Autores | Gerald Goertzel, Nunzio Tralli |
| Editor | Courier Corporation, 2014 |
| ISBN | 048679332X, 9780486793320 |
| Largo | 320 páginas |
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