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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Página 4
... constant of the spring, and x the displacement of the mass from its equilibrium position, the equation of motion of the system may be written as mjc' + kx = 0 (1.3) A system which satisfies Eq. (1.3) is called a harmonic oscillator.
... constant of the spring, and x the displacement of the mass from its equilibrium position, the equation of motion of the system may be written as mjc' + kx = 0 (1.3) A system which satisfies Eq. (1.3) is called a harmonic oscillator.
Página 8
2.1, x(t) as given by (1.21) will be found to satisfy (1.19). 1 The x, could just as well have been taken to form a 1 X n matrix or n-row. Indeed, some authors prefer the alternate choice. With this alternate choice ...
2.1, x(t) as given by (1.21) will be found to satisfy (1.19). 1 The x, could just as well have been taken to form a 1 X n matrix or n-row. Indeed, some authors prefer the alternate choice. With this alternate choice ...
Página 11
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 ...
Página 17
The ith row of p satisfies PM” = 6i. (1'43) or written out 2 mijik = 6w The matrix of coefficients is the matrix mT, so that the existence of a unique solution for each row of p follows from properties 1 and 2 taken in conjunction with ...
The ith row of p satisfies PM” = 6i. (1'43) or written out 2 mijik = 6w The matrix of coefficients is the matrix mT, so that the existence of a unique solution for each row of p follows from properties 1 and 2 taken in conjunction with ...
Página 22
a) it From (2.5) it follows that f(A)“ =f (1):: (2.8) The result given in (2.8), which holds for any u which is an eigencolumn of A [i.e. , any u satisfying (2.7)], and for any f with convergent-power-series expansion, will be the basis ...
a) it From (2.5) it follows that f(A)“ =f (1):: (2.8) The result given in (2.8), which holds for any u which is an eigencolumn of A [i.e. , any u satisfying (2.7)], and for any f with convergent-power-series expansion, will be the basis ...
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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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