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 3
... constant coefficients. There are a finite number of dependent variables (the coordinates of the physical system) and one independent variable (the time). Part One is concerned solely with the solution of such systems of equations for ...
... constant coefficients. There are a finite number of dependent variables (the coordinates of the physical system) and one independent variable (the time). Part One is concerned solely with the solution of such systems of equations for ...
Página 4
... constant of the spring, and x the displacement of the mass from its equilibrium position, the equation of motion of the system may be written as mjc' + kx = 0 (1.3) A system which satisfies Eq. (1.3) is called a harmonic oscillator. F ...
... constant of the spring, and x the displacement of the mass from its equilibrium position, the equation of motion of the system may be written as mjc' + kx = 0 (1.3) A system which satisfies Eq. (1.3) is called a harmonic oscillator. F ...
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... constants. 1.3 Matrices In each of the three categories of problems considered in Sec. 1.2, the set of n2 numbers mu played a central role. This set of numbers is given a name as an assemblage. The assemblage is said to form a matrix m ...
... constants. 1.3 Matrices In each of the three categories of problems considered in Sec. 1.2, the set of n2 numbers mu played a central role. This set of numbers is given a name as an assemblage. The assemblage is said to form a matrix m ...
Página 9
... constant will be 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 ...
... constant will be 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 ...
Página 25
... constants, whereas an arbitrary column is specified by all n elements. If A does have n linearly independent eigencolumns, it is possible to solve specifically for u in terms of the eigencolumns (see the next paragraph), thus completing ...
... constants, whereas an arbitrary column is specified by all n elements. If A does have n linearly independent eigencolumns, it is possible to solve specifically for u in terms of the eigencolumns (see the next paragraph), thus completing ...
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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