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. |
Dentro del libro
Resultados 6-10 de 46
Página 17
... relations. 1.9 Linear Independence Up to now, square matrices have been separated into two categories, singular matrices and nonsingular matrices. It is further possible to define an index, the rank of a matrix, which indicates the ...
... relations. 1.9 Linear Independence Up to now, square matrices have been separated into two categories, singular matrices and nonsingular matrices. It is further possible to define an index, the rank of a matrix, which indicates the ...
Página 32
... , written in terms of the new variables, is solved. The old variables are then calculated from their relation to the new. To see how this works, consider diagonalizable A A = 32 SYSTEMS WITH A FINITE NUMBER OF DEGREES or FREEDOM.
... , written in terms of the new variables, is solved. The old variables are then calculated from their relation to the new. To see how this works, consider diagonalizable A A = 32 SYSTEMS WITH A FINITE NUMBER OF DEGREES or FREEDOM.
Página 38
... relation: If AS = SA then f (A)S = Sf(A) This method was then applied to any matrix A for which S-1 existed and indeed ielded y f(A) = Sf(A)S" An alternate method of expressing f(A) is by means of the Cauchy-integral formula from ...
... relation: If AS = SA then f (A)S = Sf(A) This method was then applied to any matrix A for which S-1 existed and indeed ielded y f(A) = Sf(A)S" An alternate method of expressing f(A) is by means of the Cauchy-integral formula from ...
Página 44
... relations u(t) = 3Q eZ'U(Z) dZ 2111 U(Z) =fme'Z'u(t) dt 0 define an equivalence between u(t) and U(Z). U(Z) is known ... relation U(Z) =Jwe'z'u(t) dt (3.14) 0 b. Multiply Eq. (3.13) by e—Z' dt and integrate from 0 to 00. Then, the left ...
... relations u(t) = 3Q eZ'U(Z) dZ 2111 U(Z) =fme'Z'u(t) dt 0 define an equivalence between u(t) and U(Z). U(Z) is known ... relation U(Z) =Jwe'z'u(t) dt (3.14) 0 b. Multiply Eq. (3.13) by e—Z' dt and integrate from 0 to 00. Then, the left ...
Página 52
... relations (4.5) expresses the orthogonality (i.e., the mutual perpendicularity) of the base vectors 1, j, k. The second relation expresses the normality (i.e., the unit length) of the base vectors. The relations (4.5) together are known ...
... relations (4.5) expresses the orthogonality (i.e., the mutual perpendicularity) of the base vectors 1, j, k. The second relation expresses the normality (i.e., the unit length) of the base vectors. The relations (4.5) together are known ...
Otras ediciones - Ver todas
Términos y frases comunes
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