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 8
... the matrix multiplication rule of Sec. 1.4, the form of the various equations is slightly different. Thus, Eq. (1.20) would be written as 22 = xm + F (r). To illustrate the method of writing the equations of motion 8 SYSTEMS WITH A ...
... the matrix multiplication rule of Sec. 1.4, the form of the various equations is slightly different. Thus, Eq. (1.20) would be written as 22 = xm + F (r). To illustrate the method of writing the equations of motion 8 SYSTEMS WITH A ...
Página 9
... 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 12
Using the above description of the process of multiplication of a row into a column, it is not difficult to describe ... In fact, the 1'] element of mp is obtained by multiplying the ith row of m into the jth column of p: P11 P21 (mph.
Using the above description of the process of multiplication of a row into a column, it is not difficult to describe ... In fact, the 1'] element of mp is obtained by multiplying the ith row of m into the jth column of p: P11 P21 (mph.
Página 13
... in their arithmetic properties from numbers will be considered. These differences all arise from the definition of the product of two matrices. The first difference to be considered is the noncommutativity of matrix multiplication.
... in their arithmetic properties from numbers will be considered. These differences all arise from the definition of the product of two matrices. The first difference to be considered is the noncommutativity of matrix multiplication.
Página 25
It is clear that if f(A) is a known matrix, the value of f(A)u is known-for arbitrary u, since the indicated multiplication can be carried out. Similarly, if the value of f(A)u is known for arbitrary u, f(A) may be considered a known ...
It is clear that if f(A) is a known matrix, the value of f(A)u is known-for arbitrary u, since the indicated multiplication can be carried out. Similarly, if the value of f(A)u is known for arbitrary u, f(A) may be considered a known ...
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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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