## 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. |

### Dentro del libro

Resultados 1-5 de 7

Página v

In Part One of the book, systems with a

described by matrices) are considered and studied. In Part Two the concepts

developed for discrete systems in Part One are extended to continuous systems.

In Part One of the book, systems with a

**finite number**of degrees of freedom (described by matrices) are considered and studied. In Part Two the concepts

developed for discrete systems in Part One are extended to continuous systems.

Página 3

1.1 Introduction The equations of motion describing physical systems which are

linear, have a

independent of time are relatively simple in nature. (See also the last paragraph

of Sec.

1.1 Introduction The equations of motion describing physical systems which are

linear, have a

**finite number**of degrees of freedom, and have propertiesindependent of time are relatively simple in nature. (See also the last paragraph

of Sec.

Página 7

These problems are again specified by n2 quantities m,,-, but require in addition

the n numbers F,. In the first sentence of Sec. 1.] appear the words “are linear,

have a

...

These problems are again specified by n2 quantities m,,-, but require in addition

the n numbers F,. In the first sentence of Sec. 1.] appear the words “are linear,

have a

**finite number**of degrees of freedom, and have properties independent of...

Página 10

Two matrices may be equated only if each has the same number of columns and

the same number of rows as the other. ... is obtained by replacing each element

of the 10 SYSTEMS WITH A

Two matrices may be equated only if each has the same number of columns and

the same number of rows as the other. ... is obtained by replacing each element

of the 10 SYSTEMS WITH A

**FINITE NUMBER**OF DEGREES OF FREEDOM. Página 28

If the eigencolumns are linearly dependent, there exists a set of numbers a,, not

all zero, such that 2 ... 2.6 Outline of Computation Procedure with Examples The

motivation of 28 SYSTEMS WITH A

If the eigencolumns are linearly dependent, there exists a set of numbers a,, not

all zero, such that 2 ... 2.6 Outline of Computation Procedure with Examples The

motivation of 28 SYSTEMS WITH A

**FINITE NUMBER**OF DEGREES OF ...### Comentarios de la gente - Escribir un comentario

No encontramos ningún comentario en los lugares habituales.

### 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