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 14
... evaluate the determinant. It will be seen in Sec. 1.8 that nonsingular matrices have the properties mentioned earlier in this section for nonzero numbers. Thus, the product of two nonsingular matrices is nonsingular (this is a stronger ...
... evaluate the determinant. It will be seen in Sec. 1.8 that nonsingular matrices have the properties mentioned earlier in this section for nonzero numbers. Thus, the product of two nonsingular matrices is nonsingular (this is a stronger ...
Página 18
... evaluate 4 4 4 4 2 ft 2 8t fiz 8i i=1 i=1 i=1 t=1 4 2 4 4 4 210} + 3") 21. igi Zl-Ii'gii'l glfnqgi i | 1 2 3 4 5 f,- ' 1 1.5 2.1 2.8 3.6 g,- 0.7 0.9 1.2 1.6 2.1 0 1 0 i -10 10 —i 0 01 Calculate 0,, cos (p + 0,, sin 9), 0:, 0f, ...
... evaluate 4 4 4 4 2 ft 2 8t fiz 8i i=1 i=1 i=1 t=1 4 2 4 4 4 210} + 3") 21. igi Zl-Ii'gii'l glfnqgi i | 1 2 3 4 5 f,- ' 1 1.5 2.1 2.8 3.6 g,- 0.7 0.9 1.2 1.6 2.1 0 1 0 i -10 10 —i 0 01 Calculate 0,, cos (p + 0,, sin 9), 0:, 0f, ...
Página 19
... — AI is singular. 000 8.Let 6:100 0 1 0 Evaluate £2, 83, e“. 9. Find the nth power of the square matrix M defined by a. M: [3 (abc) 7 10. Verify that AB = BA if A and B. FORMULATION OF THE PROBLEM AND DEVELOPMENT OF NOTATION 19.
... — AI is singular. 000 8.Let 6:100 0 1 0 Evaluate £2, 83, e“. 9. Find the nth power of the square matrix M defined by a. M: [3 (abc) 7 10. Verify that AB = BA if A and B. FORMULATION OF THE PROBLEM AND DEVELOPMENT OF NOTATION 19.
Página 22
... evaluation. Such considerations as these further suggest the definition of the value of a function of a matrix. Thus ... evaluation of e'“ and f(A) is to be desired. Such a method of evaluation will be determined in. this chapter. (2.6) ...
... evaluation. Such considerations as these further suggest the definition of the value of a function of a matrix. Thus ... evaluation of e'“ and f(A) is to be desired. Such a method of evaluation will be determined in. this chapter. (2.6) ...
Página 23
... evaluation of the solution (2.4) of the differential equation (2.1). If it so happens that u(0) in (2.4) is an eigencolumn of A, then (2.8) yields immediately u(t) = e'“u(0) = e”u(0) (2.9) It should be noticed that the solution (2.9) is ...
... evaluation of the solution (2.4) of the differential equation (2.1). If it so happens that u(0) in (2.4) is an eigencolumn of A, then (2.8) yields immediately u(t) = e'“u(0) = e”u(0) (2.9) It should be noticed that the solution (2.9) is ...
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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