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 ix
... Definition . . . . . . . . . The Necessary and Sufficient Condition for a Green's Function The Operator —-m2d2/dx2 + I in an Infinite Domain The Operator —ar2d2ldx2 + l in a Finite Domain . The Operator “022V: + 1 in Spherical ...
... Definition . . . . . . . . . The Necessary and Sufficient Condition for a Green's Function The Operator —-m2d2/dx2 + I in an Infinite Domain The Operator —ar2d2ldx2 + l in a Finite Domain . The Operator “022V: + 1 in Spherical ...
Página 7
... define rectangular matrices. Thus, if 11,-,- is defined for all pairs of valuesiandjsuchthati = 1,2,3,. . . ,p,andj = 1,2,. . . ,n,thentheset of pn numbers q,, is said to form a rectangular p X n matrix. Such a matrix may be displayed ...
... define rectangular matrices. Thus, if 11,-,- is defined for all pairs of valuesiandjsuchthati = 1,2,3,. . . ,p,andj = 1,2,. . . ,n,thentheset of pn numbers q,, is said to form a rectangular p X n matrix. Such a matrix may be displayed ...
Página 8
... define rules for their manipulation. Such rules will be presented in some detail in Sec. 1.4. These rules are so set ... definition of e'"'. If this viewpoint be adopted, the methods of interpretation and evaluation of em' to be ...
... define rules for their manipulation. Such rules will be presented in some detail in Sec. 1.4. These rules are so set ... definition of e'"'. If this viewpoint be adopted, the methods of interpretation and evaluation of em' to be ...
Página 9
... defined. These definitions have been developed over many years. The reader of this book will note that the definitions are such as to assure that (1.19) is identical in meaning with (1.11) and that (1.20) contains the same information ...
... defined. These definitions have been developed over many years. The reader of this book will note that the definitions are such as to assure that (1.19) is identical in meaning with (1.11) and that (1.20) contains the same information ...
Página 10
... defined. First, the equality of two matrices will be discussed. Two matrices may be equated only if each has the same number of columns and the same number of rows as the other. In this case, the matrices are equal if each element of ...
... defined. First, the equality of two matrices will be discussed. Two matrices may be equated only if each has the same number of columns and the same number of rows as the other. In this case, the matrices are equal if each element of ...
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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