Some Mathematical Methods of PhysicsThis 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 7
The quantities m,,- are called the elements of the matrix m. For the purpose of display of the matrix m ... "Inn To find the element m,, one looks at the intersection of the ith row with the jth column. The matrix m is a square matrix, ...
The quantities m,,- are called the elements of the matrix m. For the purpose of display of the matrix m ... "Inn To find the element m,, one looks at the intersection of the ith row with the jth column. The matrix m is a square matrix, ...
Página 10
In this case, the matrices are equal if each element of one equals the corresponding element of the other. ... Each element of the sum matrix is obtained by adding the corresponding elements of the summand matrices.
In this case, the matrices are equal if each element of one equals the corresponding element of the other. ... Each element of the sum matrix is obtained by adding the corresponding elements of the summand matrices.
Página 11
time-dependent elements is obtained by replacing each element of the matrix with its time derivative. Thus ... Any matrix all of whose elements are zero is a zero matrix. Zero matrices have the expected properties 0+m:m OmImOZO In ...
time-dependent elements is obtained by replacing each element of the matrix with its time derivative. Thus ... Any matrix all of whose elements are zero is a zero matrix. Zero matrices have the expected properties 0+m:m OmImOZO In ...
Página 12
its elements along the main diagonal (the elements Ikk) are unity and all others are zero. That is Ii,- = 6,, (1.34) where the symbol 6,,- is the Kronecker delta symbol and is defined by the following relations 6,, = 1 6,, ...
its elements along the main diagonal (the elements Ikk) are unity and all others are zero. That is Ii,- = 6,, (1.34) where the symbol 6,,- is the Kronecker delta symbol and is defined by the following relations 6,, = 1 6,, ...
Página 14
This determinant can be calculated, if the elements of m are known. Thus, if m is a 2 X 2 matrix, _ _ 1"" = m11m22 _ m12m21 (1-40) whereas, If m 1s 3 X 3, PM = m11m22m33 + ml2m23m31 + m13m21m32 * mumzsmaz — m12m21maa _ m13m22m31 (1-41) ...
This determinant can be calculated, if the elements of m are known. Thus, if m is a 2 X 2 matrix, _ _ 1"" = m11m22 _ m12m21 (1-40) whereas, If m 1s 3 X 3, PM = m11m22m33 + ml2m23m31 + m13m21m32 * mumzsmaz — m12m21maa _ m13m22m31 (1-41) ...
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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
Información bibliográfica
| Título | Some Mathematical Methods of Physics Dover Books on Physics |
| Autores | Gerald Goertzel, Nunzio Tralli |
| Editor | Courier Corporation, 2014 |
| ISBN | 048679332X, 9780486793320 |
| Largo | 320 páginas |
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