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 3
These equations are linear differential equations with constant coefficients. There are a finite number of dependent variables (the coordinates of the physical system) and one independent variable (the time).
These equations are linear differential equations with constant coefficients. There are a finite number of dependent variables (the coordinates of the physical system) and one independent variable (the time).
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If m denotes the magnitude of the mass, k the spring 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 ...
If m denotes the magnitude of the mass, k the spring 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 ...
Página 7
The number of degrees of freedom is the number of dependent variables n, so that a finite number of degrees of freedom implies finite n. The phrase properties independent of time states that the quantities m,, are constants.
The number of degrees of freedom is the number of dependent variables n, so that a finite number of degrees of freedom implies finite n. The phrase properties independent of time states that the quantities m,, are constants.
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... 0 0 x4 1.4 Elementary Arithmetic Operations with Matrices In this section the equality of two matrices, the sum of two matrices, the product of two matrices, and the multiplication of a matrix with a constant will be defined.
... 0 0 x4 1.4 Elementary Arithmetic Operations with Matrices In this section the equality of two matrices, the sum of two matrices, the product of two matrices, and the multiplication of a matrix with a constant will be defined.
Página 25
Thus, if A has less than n linearly independent eigencolumns, the resultant linear superposition will depend on less than n arbitrary constants, whereas an arbitrary column is specified by all n elements.
Thus, if A has less than n linearly independent eigencolumns, the resultant linear superposition will depend on less than n arbitrary constants, whereas an arbitrary column is specified by all n elements.
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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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