Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página viii
... Chapter 4 Vector Spaces and Linear Operators 4.1 Introduction · 4.2 Base Vectors and Basis 43 44 46 47 50 50 52 4.3 Change of Basis 4.4 Linear Operators 4.5 The Representation of Linear Operators by Matrices 4.6 The Operator in the Dual ...
... Chapter 4 Vector Spaces and Linear Operators 4.1 Introduction · 4.2 Base Vectors and Basis 43 44 46 47 50 50 52 4.3 Change of Basis 4.4 Linear Operators 4.5 The Representation of Linear Operators by Matrices 4.6 The Operator in the Dual ...
Página ix
... Chapter 9 The Laplacian ( v2 ) in One Dimension 9.1 Introduction 105 107 108 111 111 9.2 The Infinite Domain , - -∞0 < x < + ∞ 9.4 The Finite Domain , 0 ≤x≤L . 112 9.3 The Semi - infinite Domain , 0 ≤ x < + ∞ 116 119 9.5 The ...
... Chapter 9 The Laplacian ( v2 ) in One Dimension 9.1 Introduction 105 107 108 111 111 9.2 The Infinite Domain , - -∞0 < x < + ∞ 9.4 The Finite Domain , 0 ≤x≤L . 112 9.3 The Semi - infinite Domain , 0 ≤ x < + ∞ 116 119 9.5 The ...
Página x
... Chapter 14 Perturbation of Eigenvalues 14.1 Introduction 14.2 14.3 · Formulation of the Problem A Simple Solution ... Chapter 15 Variational Estimates 15.1 Introduction 15.2 The Rayleigh Variational Principle 15.3 A Lower Bound 15.4 The ...
... Chapter 14 Perturbation of Eigenvalues 14.1 Introduction 14.2 14.3 · Formulation of the Problem A Simple Solution ... Chapter 15 Variational Estimates 15.1 Introduction 15.2 The Rayleigh Variational Principle 15.3 A Lower Bound 15.4 The ...
Contenido
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
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approximate arbitrary ax² basis Bessel function boundary conditions chap coefficients column consider constant continuous systems contour coordinates corresponding cylindrical functions d²/dx² defined denoted determinant diagonal differential equation Dirac notation domain eigen eigencolumns eigenfunctions eigenvalue equation eigenvector eikr evaluate expansion finite number follows Fourier given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral inverse Laplace transform Laplacian linear operator linearly independent lowest eigenvalue matrix membrane method multiplication nonsingular normal obtained orthonormality conditions plane problem procedure relations representation result satisfies the boundary scattering sinh solve spherical spherical harmonics string Substitution theorem trial functions vanish variable vector space Verify wave write written y₁ yields York zero ηπχ πο ποχ ди ду дх