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 7
The form of the equations for the steady-state problem is obtained from (1.16) by setting all the at, equal to zero and writing F, in place of F ,(t). These problems are again specified by n2 quantities m,,-, but require in addition the ...
The form of the equations for the steady-state problem is obtained from (1.16) by setting all the at, equal to zero and writing F, in place of F ,(t). These problems are again specified by n2 quantities m,,-, but require in addition the ...
Página 8
The n numbers x, may be considered to form an n X 1 matrix1 or n column, so that one may write x' X1 X2 X2 x : x3 it = x3 (1.18) xn )2" Similarly, the n quantities F I(t) appearing in (1.16) will be represented by the n-column F (t).
The n numbers x, may be considered to form an n X 1 matrix1 or n column, so that one may write x' X1 X2 X2 x : x3 it = x3 (1.18) xn )2" Similarly, the n quantities F I(t) appearing in (1.16) will be represented by the n-column F (t).
Página 9
To illustrate the method of writing the equations of motion suggested by the matrix notation, Eqs. (1.6) are ... it is desirable to introduce a notation which enables one to write the required relations in concise and clear form.
To illustrate the method of writing the equations of motion suggested by the matrix notation, Eqs. (1.6) are ... it is desirable to introduce a notation which enables one to write the required relations in concise and clear form.
Página 13
A convenient notation is to write mt. Similarly, the ith column ofm is written m i. The period (.) is used to indicate the position ofthe index not specified relative to the position of the specified index (i in this case).
A convenient notation is to write mt. Similarly, the ith column ofm is written m i. The period (.) is used to indicate the position ofthe index not specified relative to the position of the specified index (i in this case).
Página 23
Thus, let the eigencolumns of A be denoted s_,-, so that As, = Ls, (2.10) Further, suppose that there are enough such eigencolumns that one may write, for the specified initial conditions 14(0), “(0) = 5.1111 + 3.2% + ' ' ' = Saar ...
Thus, let the eigencolumns of A be denoted s_,-, so that As, = Ls, (2.10) Further, suppose that there are enough such eigencolumns that one may write, for the specified initial conditions 14(0), “(0) = 5.1111 + 3.2% + ' ' ' = Saar ...
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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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