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 8
... methods of interpretation and evaluation of em' to be presented below will be found consistent with its definition. Alternately, if the ... method of writing the equations of motion 8 SYSTEMS WITH A FINITE NUMBER OF DEGREES OF FREEDOM.
... methods of interpretation and evaluation of em' to be presented below will be found consistent with its definition. Alternately, if the ... method of writing the equations of motion 8 SYSTEMS WITH A FINITE NUMBER OF DEGREES OF FREEDOM.
Página 9
Gerald Goertzel, Nunzio Tralli. To illustrate the method of writing the equations of motion suggested by the matrix notation, Eqs. (1.6) are rewritten below: it, 0 c 1/m 0 x, )2 0 0 0 1 m x _2 = / 2 (1.22) x3 —k —- ko k0 0 0 x3 x, k, —-k ...
Gerald Goertzel, Nunzio Tralli. To illustrate the method of writing the equations of motion suggested by the matrix notation, Eqs. (1.6) are rewritten below: it, 0 c 1/m 0 x, )2 0 0 0 1 m x _2 = / 2 (1.22) x3 —k —- ko k0 0 0 x3 x, k, —-k ...
Página 12
... method of obtaining the if element of the matrix product mp, where m and p are any two matrices such that the number of columns of m equals the number of rows of p. In fact, the 1'] element of mp is obtained by multiplying the ith row ...
... method of obtaining the if element of the matrix product mp, where m and p are any two matrices such that the number of columns of m equals the number of rows of p. In fact, the 1'] element of mp is obtained by multiplying the ith row ...
Página 20
... Methods in Engineering,” chap. 5, McGraw-Hill Book Company, Inc., New York, 1940. Margenau, H., and G. M. Murphy: “The Mathematics of Physics and Chemistry,” chap. 10, D. Van Nostrand Company, Inc., Princeton, N.J., 1943. Jefi'reys, H ...
... Methods in Engineering,” chap. 5, McGraw-Hill Book Company, Inc., New York, 1940. Margenau, H., and G. M. Murphy: “The Mathematics of Physics and Chemistry,” chap. 10, D. Van Nostrand Company, Inc., Princeton, N.J., 1943. Jefi'reys, H ...
Página 21
... method for the solution of the differential equation 12(1) = Au(t) (2.1) yields the solution in the form of a power series in the independent variable t. Thus, as the reader will readily verify, d"u n din = A u (2.2) whence, using the ...
... method for the solution of the differential equation 12(1) = Au(t) (2.1) yields the solution in the form of a power series in the independent variable t. Thus, as the reader will readily verify, d"u n din = A u (2.2) whence, using the ...
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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