Some Mathematical Methods of PhysicsCourier Corporation, 2014 M03 5 - 320 páginas This 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
... linear, have a finite number of degrees of freedom, and have properties independent of time are relatively simple in nature. (See also the last paragraph of Sec. 1.2.) These equations are linear differential equations with constant ...
... linear, have a finite number of degrees of freedom, and have properties independent of time are relatively simple in nature. (See also the last paragraph of Sec. 1.2.) These equations are linear differential equations with constant ...
Página 5
... independent inhomogeneous (steady-state) problems of (1.9) and (1.10). For each of these categories, the corresponding equations have a definite form. For the linear time-dependent homogeneous problems, the equations of motion may ...
... independent inhomogeneous (steady-state) problems of (1.9) and (1.10). For each of these categories, the corresponding equations have a definite form. For the linear time-dependent homogeneous problems, the equations of motion may ...
Página 7
... linear, have a finite number of degrees of freedom, and have properties independent of time.” The limitations implied by these words are readily interpreted with the aid of Eqs. (1.16). Linear implies that each term in(l .16) contains ...
... linear, have a finite number of degrees of freedom, and have properties independent of time.” The limitations implied by these words are readily interpreted with the aid of Eqs. (1.16). Linear implies that each term in(l .16) contains ...
Página 18
... linear superposition of the columns of the matrix. To proceed further, it is useful to introduce the concept of linear independence. A set of n columns is said to be linearly independent if there exists no linear combination of these ...
... linear superposition of the columns of the matrix. To proceed further, it is useful to introduce the concept of linear independence. A set of n columns is said to be linearly independent if there exists no linear combination of these ...
Página 25
... linearly independent eigencolumns. 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 ...
... linearly independent eigencolumns. 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 ...
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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