Index Index
amplitude
definition, Definition
ansatz
definition, Definition
homogeneous, linear ODE with constant coefficients, Paragraphs
inhomogeneous, linear ODE with constant coefficients, Paragraphs Paragraphs Paragraphs
power series solutions for ODEs, Paragraph
associated Laguerre polynomial
definition, Paragraph
Associated Legendre Functions
definition, Paragraph
properties, Paragraph
binomial coefficients
definition, Paragraph
boundary conditions
Dirichlet, definition, Paragraph
Neumann, definition, Paragraph
periodic, definition, Paragraph
boundary value problem, Definition
central force
definition, Definition
characteristic equation
for linear ODEs with constant coefficients, Definition
complete basis
definition, Definition
degeneracy
in ODEs, Paragraphs
in the quadratic formula, Definition
differential equation
definition, Definition
degree of, Definition
general solution, Definition
homogeneous, Definition
inhomogeneous, Definition
order of, Definition
ordinary, Definition
partial, Definition
particular solution, Definition
solution of, Definition
differential operator
linear, Notation
diffusion equation, Paragraphs
Dirichlet boundary conditions
definition, Paragraph
effective potential
definition, Paragraph
first-order ODEs
differential form, Definition
separable form, Definition
standard form, Definition
forcing function
in an ODE, Paragraphs
Helmholtz’s equation, Paragraphs
inhomogeneous
in an ODE, Paragraphs
initial value problem, Definition
inner product
definition, Definition
Fourier series, Definition
Klein-Gordon equation, Paragraphs
Laguerre polynomial
definition, Paragraph
Laplace’s equation, Paragraphs
Legendre polynomial
definition, Paragraph
Legendre polynomials
definiton, Definition
Legendre’s associated equation
definition, Paragraph
Legendre’s equation
definition, Definition
formula, Paragraph
power series solution, Section
length
of abstract vectors, Paragraph
linear ODEs with constant coefficients
solution method, homogeneous, Paragraphs
solution method, inhomogeneous, Paragraphs
linear operator
definition, Definition
derivatives as, Paragraphs
Hermitian operators as, Paragraphs
matrices as, Paragraphs
momentum of center of mass
definition, Definition
negative vector, Item
Neumann boundary conditions
definition, Paragraph
non-interacting particles
definition, Paragraph
norm
of abstract vectors, Paragraph
null vector
definition, Item
orthogonal
for abstract vectors, Paragraph
for functions, Definition
orthogonal polynomial
Laguerre, Paragraph
orthogonal polyomial
associated Laguerre, Paragraph
partial differential equations
diffusion equation, Paragraphs
Helmholtz’s equation, Paragraphs
Klein-Gordon equation, Paragraphs
Laplace’s equation, Paragraphs
Poisson’s equation, Paragraphs
Schrödinger’s equation, Paragraphs
wave equation, Paragraphs
periodic boundary conditions
definition, Paragraph
perpendicular
for abstract vectors, Paragraph
phase
definition, Definition
Poisson’s equation, Paragraphs
position of center of mass
definition, Definition
recurrence relation
definiton, Definition
for Legendre’s equation, Definition
reduced mass
definition, Definition
regular point of an ODE
definition, Definition
regular singularity of an ODE
definition, Definition
Rodrigues’ Formula
for Legendre polynomials, Paragraph
Rodrigues’ formula
for Laguerre polynomials, Paragraph
scalar identity
in a vector space, Item
Schrödinger’s equation, Paragraphs
separation constants, Paragraphs
separation of variables
definition, Definition
method, Section
separation of variables in PDEs
separation constants, Paragraphs
source
in an ODE, Paragraphs
spherical harmonics
algebraic definition, Paragraph
graphs, Section
Sturm-Liouville theory
introduction, Paragraph
Sturm–Liouville theory, Section
torque
definition, Definition
