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 6
... vanish. The second category, that of time-dependent inhomogeneous problems, has equations of the form given by (1.16) below. It will be noted that setting F,(t) = 0 reduces these to (1.11). 1 *1 = mllxl + "112x2 '1' ' ' ' + mlnxn + F10 ...
... vanish. The second category, that of time-dependent inhomogeneous problems, has equations of the form given by (1.16) below. It will be noted that setting F,(t) = 0 reduces these to (1.11). 1 *1 = mllxl + "112x2 '1' ' ' ' + mlnxn + F10 ...
Página 15
... vanish for at most n values of 2. We may further deduce that |I| = 1. Thus, if m is a nonsingular matrix, since ml = m one has from property 4 WI |1 I = lml whence VI = 1 1.8 Inverses We now show that the product of two. 1 The ...
... vanish for at most n values of 2. We may further deduce that |I| = 1. Thus, if m is a nonsingular matrix, since ml = m one has from property 4 WI |1 I = lml whence VI = 1 1.8 Inverses We now show that the product of two. 1 The ...
Página 16
... vanish) there exists a unique matrix, denoted by m-l, such that mm—1 : m—lm = 1. Thus, it will first be shown that there exists a q such that mq I I, second that there exists a p such that pm = I, and third that p = q. To find q such ...
... vanish) there exists a unique matrix, denoted by m-l, such that mm—1 : m—lm = 1. Thus, it will first be shown that there exists a q such that mq I I, second that there exists a p such that pm = I, and third that p = q. To find q such ...
Página 17
... vanish. This inverse may be written explicitly in usable form for 2 X 2 and 3 x 3 nonsingular matrices. Let D denote the determinant of m [as given in (1.40) or (1.41)]. For 2 X 2 matrices _ 1 "'22 —m12 m 1 = — (1.44) _ D “'mzt mu For 3 ...
... vanish. This inverse may be written explicitly in usable form for 2 X 2 and 3 x 3 nonsingular matrices. Let D denote the determinant of m [as given in (1.40) or (1.41)]. For 2 X 2 matrices _ 1 "'22 —m12 m 1 = — (1.44) _ D “'mzt mu For 3 ...
Página 27
... vanish. Thus, it must be that. [Al. _. AI. = 0. (2.24). Hence, before a solution to (2.23) can exist, it is necessary that the eigenvalue be so chosen as to satisfy (2.24). This determinantal equation is called the characteristic equation ...
... vanish. Thus, it must be that. [Al. _. AI. = 0. (2.24). Hence, before a solution to (2.23) can exist, it is necessary that the eigenvalue be so chosen as to satisfy (2.24). This determinantal equation is called the characteristic equation ...
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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