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 4
... given indefinitely, those already presented will suffice to give a picture of the situation. It is of interest to note that some of the above examples contain only first derivatives with respect to the time, whereas others contain ...
... given indefinitely, those already presented will suffice to give a picture of the situation. It is of interest to note that some of the above examples contain only first derivatives with respect to the time, whereas others contain ...
Página 6
... given in (1.1 l), by the number of dependent variablesn, and by the n2 numbers m“, i, and j taking on the n values 1, 2, . . . , n — 1, n independently. As can be seen from the examples, many of the numbers m,,- may vanish. The second ...
... given in (1.1 l), by the number of dependent variablesn, and by the n2 numbers m“, i, and j taking on the n values 1, 2, . . . , n — 1, n independently. As can be seen from the examples, many of the numbers m,,- may vanish. The second ...
Página 8
... given in Sec. 2.1, x(t) as given by (1.21) will be found to satisfy (1.19). 1 The x, could just as well have been taken to form a 1 X n matrix or n-row. Indeed, some authors prefer the alternate choice. With this alternate choice and ...
... given in Sec. 2.1, x(t) as given by (1.21) will be found to satisfy (1.19). 1 The x, could just as well have been taken to form a 1 X n matrix or n-row. Indeed, some authors prefer the alternate choice. With this alternate choice and ...
Página 11
... given here. The product of two matrices is defined only if the number of columns in the matrix on the left is equal to the number of rows in the matrix on the right. The product is then defined by (1.28) ("Ulla = 2 mtkPkt " (1.29) (mx)r ...
... given here. The product of two matrices is defined only if the number of columns in the matrix on the left is equal to the number of rows in the matrix on the right. The product is then defined by (1.28) ("Ulla = 2 mtkPkt " (1.29) (mx)r ...
Página 12
... given by Eqs. (1.29), is also the rule for the calculation of the product. To understand this rule, one might consider the result it gives for the product of a l X n matrix (row) 2 with an n X 1- matrix (column) x. The result is a 1 X 1 ...
... given by Eqs. (1.29), is also the rule for the calculation of the product. To understand this rule, one might consider the result it gives for the product of a l X n matrix (row) 2 with an n X 1- matrix (column) x. The result is a 1 X 1 ...
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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