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 12
... (column) x. The result is a 1 X 1 matrix zx given by 2x = Zzixi (1.37) i=1 In words the prescription becomes: To multiply the row 2 into the column x, multiply the leftmost element of 2 by the topmost element of x; then multiply the ...
... (column) x. The result is a 1 X 1 matrix zx given by 2x = Zzixi (1.37) i=1 In words the prescription becomes: To multiply the row 2 into the column x, multiply the leftmost element of 2 by the topmost element of x; then multiply the ...
Página 13
... 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). Using this notation, one has as the rule for forming the product of ...
... 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). Using this notation, one has as the rule for forming the product of ...
Página 16
... columns of q in turn. These are mqa' : (54' (1-42) for the ith column of q. Written out, they become 2 miqui = 6n ,_. As follows directly from property 2, these equations have a unique solution for each column of q. Thus there exists a ...
... columns of q in turn. These are mqa' : (54' (1-42) for the ith column of q. Written out, they become 2 miqui = 6n ,_. As follows directly from property 2, these equations have a unique solution for each column of q. Thus there exists a ...
Página 17
... i.e., for those y which may be written as a linear superposition of the columns of m y _—_= 2 m'ix'. (1.47) A nonsingular matrix may be characterized by the statement that FORMULATION OF THE PROBLEM AND DEVELOPMENT OF NOTATION 17.
... i.e., for those y which may be written as a linear superposition of the columns of m y _—_= 2 m'ix'. (1.47) A nonsingular matrix may be characterized by the statement that FORMULATION OF THE PROBLEM AND DEVELOPMENT OF NOTATION 17.
Página 18
... column y can be written as a 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 ...
... column y can be written as a 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 ...
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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