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 11
... definition will be given here. The product of two matrices is defined only if the number of columns in the matrix on the left is equal to the number of rows in the matrix on the right. The product is then defined by (1.28) ("Ulla = 2 ...
... definition will be given here. The product of two matrices is defined only if the number of columns in the matrix on the left is equal to the number of rows in the matrix on the right. The product is then defined by (1.28) ("Ulla = 2 ...
Página 12
... defined by the following relations 6,, = 1 6,, = 0 for 1' 7i j The importance of the Kronecker delta arises from (1.34) and from the corresponding property (135) 2 drift =ft (1.36) 1.5 The Row-Column Rule The definition of the product ...
... defined by the following relations 6,, = 1 6,, = 0 for 1' 7i j The importance of the Kronecker delta arises from (1.34) and from the corresponding property (135) 2 drift =ft (1.36) 1.5 The Row-Column Rule The definition of the product ...
Página 13
... definition of the product of two matrices. The first difference to be considered is the noncommutativity of matrix multiplication. That is, there are matrices p and m such that mp oé pm In fact, an example of such a pair of matrices is ...
... definition of the product of two matrices. The first difference to be considered is the noncommutativity of matrix multiplication. That is, there are matrices p and m such that mp oé pm In fact, an example of such a pair of matrices is ...
Página 14
... define a singular matrix is as follows: A matrix is singular if and only if its determinantis zero. This definition yields also a test to tell when a matrix is singular—1e, one need merely evaluate the determinant. It will be seen in ...
... define a singular matrix is as follows: A matrix is singular if and only if its determinantis zero. This definition yields also a test to tell when a matrix is singular—1e, one need merely evaluate the determinant. It will be seen in ...
Página 15
Gerald Goertzel, Nunzio Tralli. The general definition of the determinant of m is given in Appendix 1A. Some ... defined by (mT),, = m”. 2. The necessary and sufficient condition that n simultaneous linear algebraic equations in ...
Gerald Goertzel, Nunzio Tralli. The general definition of the determinant of m is given in Appendix 1A. Some ... defined by (mT),, = m”. 2. The necessary and sufficient condition that n simultaneous linear algebraic equations in ...
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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