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 6
... number of dependent variablesn, and by the n2 numbers m“, i, and j taking on the n values 1, 2, . . . , n — 1, n independently. As can be seen from the examples, many of the numbers m,,- may vanish. The ... FINITE NUMBER OF DEGREE OF FREEDOM.
... number of dependent variablesn, and by the n2 numbers m“, i, and j taking on the n values 1, 2, . . . , n — 1, n independently. As can be seen from the examples, many of the numbers m,,- may vanish. The ... FINITE NUMBER OF DEGREE OF FREEDOM.
Página 7
... 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. 1.3 Matrices In ...
... 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. 1.3 Matrices In ...
Página 8
... 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 ... FINITE NUMBER OF DEGREES OF FREEDOM.
... 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 ... FINITE NUMBER OF DEGREES OF FREEDOM.
Página 10
... number of columns and the same number of rows as the other. In this case, the matrices are equal if each element of one equals the corresponding element of the other. Thus, if m and p are matrices and ... FINITE NUMBER OF DEGREES OF FREEDOM.
... number of columns and the same number of rows as the other. In this case, the matrices are equal if each element of one equals the corresponding element of the other. Thus, if m and p are matrices and ... FINITE NUMBER OF DEGREES OF FREEDOM.
Página 12
... number is the product zx. An example is given below in (1.38). Using the above description of the process of multiplication of a row into a column, it is not difficult to describe the method of ... FINITE NUMBER OF DEGREES OF FREEDOM.
... number is the product zx. An example is given below in (1.38). Using the above description of the process of multiplication of a row into a column, it is not difficult to describe the method of ... FINITE NUMBER OF DEGREES OF FREEDOM.
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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