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 20
Show that if M = AAT, then M -—- M T and hence M is a symmetric matrix. 17. Show that a nonsquare matrix cannot have an inverse. 18. Verify that the elements of the inverse of a matrix M are given by ME W I where M j, ...
Show that if M = AAT, then M -—- M T and hence M is a symmetric matrix. 17. Show that a nonsquare matrix cannot have an inverse. 18. Verify that the elements of the inverse of a matrix M are given by ME W I where M j, ...
Página 27
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 for the matrix A. Sometimes it is known as the ...
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 for the matrix A. Sometimes it is known as the ...
Página 42
1 Hence 94' = e4“ __ __ § __. 411=1122=ZII (112:0 3 1121: (Z — 1)” 42 SYSTEMS WITH A FINITE NUMBER OF DEGREE 0F FREEDOM.
1 Hence 94' = e4“ __ __ § __. 411=1122=ZII (112:0 3 1121: (Z — 1)” 42 SYSTEMS WITH A FINITE NUMBER OF DEGREE 0F FREEDOM.
Página 43
1 Hence 94' = e4“ __ __ § __ Zr dz __ i ( )11 ( )22 27". Z l e e (eA'ha = 0 = 3te' z=1 r __1_ 3 r _ i t (8A)fl_21ri§(Z—1)2ez dZ_3dZez e' 0 3te' e' The point to be noted is the appearance of a term proportional to te'.
1 Hence 94' = e4“ __ __ § __ Zr dz __ i ( )11 ( )22 27". Z l e e (eA'ha = 0 = 3te' z=1 r __1_ 3 r _ i t (8A)fl_21ri§(Z—1)2ez dZ_3dZez e' 0 3te' e' The point to be noted is the appearance of a term proportional to te'.
Página 45
The right-hand member becomes fwAu(t)e'Z' dt = AU(Z) 0 Hence 20(2) _ u(O) = AU(Z) (3.15) as in (3.11a). c. Solve Eq. (3.15) for U(Z). d. Calculate u(t) = j; eZ'U(Z) dZ (3.16) 2111 . This procedure can also be applied to equations which ...
The right-hand member becomes fwAu(t)e'Z' dt = AU(Z) 0 Hence 20(2) _ u(O) = AU(Z) (3.15) as in (3.11a). c. Solve Eq. (3.15) for U(Z). d. Calculate u(t) = j; eZ'U(Z) dZ (3.16) 2111 . This procedure can also be applied to equations which ...
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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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