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 7
... writing F, in place of F ,(t). These problems are again specified by n2 quantities m,,-, but require in addition the ... writes mu "112 "'13 ' ' ' m1" "121 11122 mm ' ' ' mu m = _ _ _ (1.17) mai "'32 mas m3n mnl mn2 mn3 ' . . "Inn To ...
... writing F, in place of F ,(t). These problems are again specified by n2 quantities m,,-, but require in addition the ... writes mu "112 "'13 ' ' ' m1" "121 11122 mm ' ' ' mu m = _ _ _ (1.17) mai "'32 mas m3n mnl mn2 mn3 ' . . "Inn To ...
Página 8
... write x' X1 X2 X2 x : x3 it = x3 (1.18) xn )2" Similarly, the n quantities F I(t) appearing in (1.16) will be ... writing the equations of motion 8 SYSTEMS WITH A FINITE NUMBER OF DEGREES OF FREEDOM.
... write x' X1 X2 X2 x : x3 it = x3 (1.18) xn )2" Similarly, the n quantities F I(t) appearing in (1.16) will be ... writing the equations of motion 8 SYSTEMS WITH A FINITE NUMBER OF DEGREES OF FREEDOM.
Página 9
... write the required relations in concise and clear form. The new concept is the summation symbol 2. Let ,, i = 1, 2 ... write 1f the summation 7, 7i variable is clear but not the range of summation, one may write In many instances the ...
... write the required relations in concise and clear form. The new concept is the summation symbol 2. Let ,, i = 1, 2 ... write 1f the summation 7, 7i variable is clear but not the range of summation, one may write In many instances the ...
Página 13
... write mt. Similarly, the ith column ofm is written m i. The period (.) is used to indicate the position ofthe index not specified relative to the position of the specified index (i in this case). Using this notation, one has as the rule ...
... write mt. Similarly, the ith column ofm is written m i. The period (.) is used to indicate the position ofthe index not specified relative to the position of the specified index (i in this case). Using this notation, one has as the rule ...
Página 23
... write, for the specified initial conditions 14(0), “(0) = 5.1111 + 3.2% + ' ' ' = Saar (2-11) In this case, the evaluation of u(t) is straightforward. u(t) = eA'u(O) = e““s_1al + e“'s_2a2 + ' ~ - = ei'l'sla1 + e'lf'sja2 + ' - ' = e1"s_ ...
... write, for the specified initial conditions 14(0), “(0) = 5.1111 + 3.2% + ' ' ' = Saar (2-11) In this case, the evaluation of u(t) is straightforward. u(t) = eA'u(O) = e““s_1al + e“'s_2a2 + ' ~ - = ei'l'sla1 + e'lf'sja2 + ' - ' = e1"s_ ...
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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