Quantum Mechanics for Engineers 4.2 alpha
© Leon van Dommelen
Index
C.
C.
C.
C.
C.
C.
C.
C.
1
.
3
|
C.
C.
C.
C.
C.
C.
C.
C.
C.
C.
C.
C.
C.
C.
C.
C.
C.
C.
C.
C.
C.
C.
C.
C.
C.
C.
C.
C.
C.
C.
C.
C.
C.
C.
C.
C.
C.
C.
21 cm line
derivation
10
.
1
.
6
.
4
intro
10
.
1
.
6
C.
C.
C.
C.
C.
C.
C.
C.
C.
Å
C.
C.
C.
absolute value
1
.
1
absolute zero
nonzero energy
2
.
6
.
3
requires ground state
8
.
1
absorption
incoherent radiation
5
.
3
.
9
single weak wave
5
.
3
.
8
absorptivity
8
.
14
.
5
acceleration
in quantum mechanics
5
.
1
.
8
action
A.
3
.
3
relativistic
see
special relativity
activation energy
radicals
4
.
2
.
6
adiabatic
disambiguation
C.
quantum mechanics
5
.
1
.
9
thermodynamics
8
.
10
adiabatic surfaces
6
.
2
.
3
adiabatic theorem
derivation and implications
A.
37
intro
5
.
1
.
9
adjoint
C.
matrices
C.
Aharonov-Bohm effect
9
.
3
Airy functions
application
A.
45
connection formulae
A.
47
graphs
A.
47
software
A.
45
alpha
see
ammonia molecule
4
.
3
amplitude
quantum
2
.
1
angle
C.
angular frequency
5
.
5
.
4
angular momentum
3
.
1
addition
9
.
1
.
6
Clebsch-Gordan coefficients
9
.
1
.
6
intro
5
.
3
.
6
advanced treatment
9
.
1
component
3
.
1
.
2
eigenfunctions
3
.
1
.
2
eigenvalues
3
.
1
.
2
conservation
5
.
3
.
6
definition
3
.
1
.
1
fundamental commutation relations
as an axiom
9
.
1
.
1
intro
3
.
4
.
4
ladder operators
9
.
1
.
2
ladders
9
.
1
.
2
normalization factors
9
.
1
.
4
operator
Cartesian
3
.
1
.
1
possible values
9
.
1
.
3
spin
4
.
4
square angular momentum
3
.
1
.
3
eigenfunctions
3
.
1
.
3
eigenvalues
3
.
1
.
3
symmetry and conservation
5
.
2
triangle inequality
intro
5
.
3
.
6
uncertainty
3
.
1
.
4
anomalous magnetic moment
9
.
6
anti-bonding
7
.
5
anticommutator
10
.
2
.
2
.
1
antisymmetrization requirement
4
.
6
graphical depiction
8
.
2
indistinguishable particles
8
.
2
number of terms
4
.
7
using groupings
4
.
7
using occupation numbers
10
.
2
.
1
using Slater determinants
4
.
7
atomic number
4
.
9
atoms
eigenfunctions
4
.
9
.
2
eigenvalues
4
.
9
.
2
ground state
4
.
9
.
3
Hamiltonian
4
.
9
.
1
average
versus expectation value
3
.
3
.
1
Avogadro's number
C.
azimuthal quantum number
3
.
1
.
3
C.
C.
Balmer transitions
3
.
2
.
3
band gap
7
.
3
band structure
crossing bands
7
.
5
intro
7
.
3
nearly-free electrons
7
.
8
widely spaced atoms
7
.
4
.
2
baryon
4
.
4
basis
C.
crystal
see
lattice, basis
spin states
4
.
5
.
6
vectors or functions
1
.
6
bcc
see
lattice
Bell's theorem
11
.
2
cheat
11
.
2
benzene molecular ring
4
.
3
Berry's phase
A.
37
.
2
Bessel functions
spherical
A.
48
.
1
beta
see
binding energy
definition
3
.
5
.
6
hydrogen molecular ion
3
.
5
.
6
hydrogen molecule
4
.
2
.
6
lithium hydride
4
.
3
Biot-Savart law
9
.
5
.
5
derivation
A.
93
.
8
blackbody radiation
8
.
14
.
5
intro
7
.
9
blackbody spectrum
8
.
14
.
5
Bloch function
free electron gas
7
.
6
.
6
nearly-free electrons
7
.
8
one-dimensional lattice
7
.
4
.
5
three-dimensional lattice
7
.
4
.
11
Bloch's theorem
7
.
4
.
5
body-centered cubic
see
lattice
Bohm
EPR experiment
11
.
2
Bohr energies
3
.
2
.
3
relativistic corrections
10
.
1
.
6
Bohr magneton
9
.
6
Bohr radius
3
.
2
.
4
Boltzmann constant
C.
Boltzmann factor
8
.
5
bond
covalent
4
.
11
.
1
hydrogen
4
.
11
.
3
ionic
4
.
11
.
5
pi
4
.
11
.
2
polar
4
.
11
.
3
sigma
4
.
11
.
1
Van der Waals
7
.
1
bond length
definition
3
.
5
.
6
hydrogen molecular ion
3
.
5
.
7
hydrogen molecule
4
.
2
.
6
Born
approximation
A.
48
.
2
series
A.
48
.
3
Born statistical interpretation
2
.
1
Born-Oppenheimer approximation
basic idea
6
.
2
.
2
derivation
6
.
2
diagonal correction
A.
53
hydrogen molecular ion
3
.
5
.
1
hydrogen molecule
4
.
2
.
1
include nuclear motion
6
.
2
.
3
relation to adiabatic theorem
5
.
1
.
9
spin degeneracy
A.
52
vibronic coupling terms
A.
53
Bose-Einstein condensation
derivation
8
.
14
.
1
intro
7
.
9
superfluidity
7
.
9
|
A.
64
Bose-Einstein distribution
7
.
9
blackbody radiation
7
.
9
|
8
.
14
.
5
canonical probability
8
.
5
for given energy
8
.
4
identify chemical potential
8
.
13
bosons
4
.
4
statistics
7
.
9
symmetrization requirement
4
.
6
bound states
hydrogen
energies
3
.
2
.
3
boundary conditions
acceptable singularity
A.
10
hydrogen atom
A.
17
across delta function potential
A.
45
at infinity
harmonic oscillator
A.
12
hydrogen atom
A.
17
impenetrable wall
2
.
5
.
4
radiation
A.
45
accelerating potential
A.
45
three-dimensional
A.
48
unbounded potential
A.
45
bra
1
.
3
|
C.
Bragg diffraction
electrons
7
.
10
.
3
Bragg planes
Brillouin fragment boundaries
7
.
4
.
11
energy singularities
7
.
8
.
2
one-dimensional (Bragg points)
7
.
4
.
7
X-ray diffraction
7
.
10
.
3
Bragg’s law
7
.
10
.
3
Brillouin zone
one-dimensional
7
.
4
.
7
three-dimensional
7
.
4
.
11
C
C.
C.
C.
canonical commutation relation
3
.
4
.
3
canonical Hartree-Fock equations
6
.
3
.
4
canonical momentum
see
special relativity
intro
5
.
1
.
10
with a magnetic field
9
.
3
canonical probability distribution
8
.
5
Carnot cycle
8
.
9
cat, Schrödinger’s
11
.
1
Cauchy-Schwartz inequality
C.
charge
electrostatics
9
.
5
.
1
chemical bonds
4
.
11
covalent pi bonds
4
.
11
.
2
covalent sigma bonds
4
.
11
.
1
hybridization
4
.
11
.
4
ionic bonds
4
.
11
.
5
polar covalent bonds
4
.
11
.
3
promotion
4
.
11
.
4
sp
hybridization
4
.
11
.
4
chemical equilibrium
constant pressure
8
.
12
constant volume
8
.
12
chemical potential
7
.
9
|
8
.
12
and distributions
8
.
13
microscopic
8
.
13
chi
see
classical
C.
Clausius-Clapeyron equation
8
.
12
Clebsch-Gordan coefficients
9
.
1
.
6
coefficient of performance
8
.
9
coefficients of eigenfunctions
evaluating
2
.
6
.
6
give probabilities
2
.
4
.
2
time variation
5
.
1
.
1
collapse of the wave function
2
.
4
.
1
collision-dominated regime
5
.
3
.
9
collisionless regime
5
.
3
.
8
color force
gluon exchange
intro
5
.
1
.
5
commutation relation
canonical
3
.
4
.
3
commutator
3
.
4
definition
3
.
4
.
2
commutator eigenvalue problems
9
.
1
.
2
commuting operators
3
.
4
.
1
common eigenfunctions
3
.
4
.
1
complete set
1
.
6
complex conjugate
1
.
1
complex numbers
1
.
1
component waves
5
.
5
.
2
components of a vector
1
.
2
conduction band
7
.
3
conduction of electricity
intro
7
.
3
confined electrons
7
.
6
confinement
2
.
5
.
9
|
7
.
6
.
5
density of states
7
.
6
.
5
connection formulae
A.
47
|
A.
47
conservation laws
and symmetries
5
.
2
conventional cell
7
.
4
.
11
Copenhagen Interpretation
2
.
4
.
1
correlation energy
6
.
3
.
5
.
4
cos
C.
Coulomb integrals
6
.
3
.
3
Coulomb potential
3
.
2
.
1
covalent bond
hydrogen molecular ion
3
.
5
covalent solids
7
.
5
creationists
A.
73
cross product
C.
crystal
lattice
see
lattice
one-dimensional
primitive translation vector
7
.
4
.
5
three-dimensional
primitive vectors
7
.
4
.
11
curl
C.
C.
C.
|
C.
C.
|
C.
Darwin term
10
.
1
.
6
.
1
Debye model
8
.
14
.
6
Debye temperature
7
.
10
.
1
|
8
.
14
.
6
degeneracy
2
.
6
.
5
degeneracy pressure
7
.
6
|
7
.
6
.
4
Delta
see
|
see
delta function
5
.
4
.
1
three-dimensional
5
.
4
.
1
density
mass
8
.
7
molar
8
.
7
particle
8
.
7
density of states
7
.
6
.
5
derivative
C.
determinant
C.
diamagnetic contribution
9
.
6
diamond
band gap
7
.
5
differential cross-section
A.
48
dipole
9
.
5
.
2
dipole strength
molecules
7
.
1
Dirac delta function
5
.
4
.
1
Dirac equation
9
.
2
Dirac notation
1
.
7
.
1
dispersion relation
5
.
5
.
4
div
C.
divergence theorem
C.
|
C.
dot product
1
.
3
doublet states
4
.
5
.
6
dynamic phase
A.
37
.
2
C.
C.
effective mass
hydrogen atom electron
3
.
2
.
1
Ehrenfest theorem
5
.
1
.
8
C.
eigenfunction
1
.
5
eigenfunctions
angular momentum component
3
.
1
.
2
atoms
4
.
9
.
2
free electron gas
7
.
6
.
3
harmonic oscillator
2
.
6
.
4
hydrogen atom
3
.
2
.
4
linear momentum
5
.
4
.
2
position
5
.
4
.
1
square angular momentum
3
.
1
.
3
eigenvalue
1
.
5
eigenvalue problems
commutator type
9
.
1
.
2
ladder operators
9
.
1
.
2
eigenvalues
angular momentum component
3
.
1
.
2
atoms
4
.
9
.
2
free electron gas
7
.
6
.
3
harmonic oscillator
2
.
6
.
3
hydrogen atom
3
.
2
.
3
linear momentum
5
.
4
.
2
position
5
.
4
.
1
square angular momentum
3
.
1
.
3
eigenvector
1
.
5
|
C.
Einstein
dice
2
.
4
.
2
mass-energy relation
see
special relativity
summation convention
A.
4
.
7
swiped special relativity
A.
4
.
1
Einstein A and B coefficients
5
.
3
.
9
Einstein's derivation
5
.
3
.
10
Einstein A coefficients
quantum derivation
10
.
2
.
4
Einstein B coefficients
quantum derivation
A.
42
Einstein Podolski Rosen
11
.
2
electric charge
electron and proton
3
.
2
.
1
electric dipole transitions
intro
5
.
3
.
4
selection rules
see
selection@ rules
electric potential
classical derivation
emph
9
.
4
|
A.
93
.
1
quantum derivation
emph
9
.
3
relativistic derivation
emph
A.
4
.
10
electric quadrupole transitions
Hamiltonian
A.
40
intro
5
.
3
.
5
selection rules
see
selection rules
electricity
conduction
intro
7
.
3
electromagnetic field
energy
10
.
2
.
3
.
1
Hamiltonian
9
.
3
Maxwell's equations
9
.
4
quantized
10
.
2
.
3
.
2
electromagnetic potentials
gauge transformation
A.
4
.
10
electromagnetic waves
quantized
10
.
2
.
3
.
4
electron
in magnetic field
9
.
6
electron affinity
7
.
2
Hartree-Fock
6
.
3
.
5
.
1
electronegativity
4
.
9
.
4
|
7
.
2
atoms
4
.
9
.
4
emission of radiation
5
.
3
.
2
emissivity
8
.
14
.
5
energy conservation
5
.
1
.
3
energy spectrum
free electron gas
7
.
6
.
3
harmonic oscillator
2
.
6
.
3
hydrogen atom
3
.
2
.
3
energy-time uncertainty relation
decay of a state
emph
5
.
1
.
6
Mandelshtam-Tamm version
5
.
1
.
7
enthalpy
8
.
7
enthalpy of vaporization
8
.
12
entropy
8
.
10
descriptive
8
.
8
EPR
11
.
2
epsilon
see
,
equipartition theorem
7
.
10
.
1
eta
see
Euler formula
1
.
1
eV
C.
Everett, III
11
.
5
every possible combination
4
.
1
|
4
.
5
.
1
exchange force mechanism
and two-state systems
5
.
1
.
5
exchange integrals
6
.
3
.
3
exchange operator
4
.
2
.
6
exchange terms
see
twilight terms
excited determinants
6
.
3
.
5
.
4
exclusion principle
4
.
7
exclusion-principle repulsion
4
.
10
expectation value
3
.
3
definition
3
.
3
.
2
simplified expression
3
.
3
.
3
versus average
3
.
3
.
1
exponential function
C.
exponential of an operator
5
.
1
.
10
extended zone scheme
7
.
7
.
2
extensive variable
8
.
7
C.
face centered cubic
see
lattice
factorial
C.
fcc
see
lattice
Fermi surface
confined boundary conditions
7
.
6
.
3
periodic boundary conditions
7
.
7
.
2
periodic zone scheme
7
.
7
.
2
reduced zone scheme
7
.
7
.
2
Fermi temperature
8
.
14
.
2
Fermi-Dirac distribution
7
.
9
canonical probability
8
.
5
for given energy
8
.
4
identify chemical potential
8
.
13
fermions
4
.
4
antisymmetrization requirement
4
.
6
statistics
7
.
9
Feynman diagrams
A.
48
.
3
field operators
10
.
2
.
5
filled shells
9
.
1
.
8
filtering property
5
.
4
.
1
fine structure
10
.
1
.
6
hydrogen atom
10
.
1
.
6
fine structure constant
10
.
1
.
6
first law of thermodynamics
8
.
1
|
8
.
7
flopping frequency
9
.
8
.
4
Floquet theory
7
.
4
.
5
Fock operator
6
.
3
.
4
Fock state
10
.
2
.
1
forbidden transitions
5
.
3
.
4
force
in quantum mechanics
5
.
1
.
8
four-vectors
see
special relativity
Fourier analysis
7
.
4
.
6
Fourier coefficients
A.
5
Fourier integral
A.
5
Fourier series
A.
5
Fourier transform
5
.
5
.
4
|
A.
5
free electron gas
7
.
6
Bloch function
7
.
6
.
6
eigenfunctions
7
.
6
.
3
eigenvalues
7
.
6
.
3
energy spectrum
7
.
6
.
3
ground state
7
.
6
.
3
Hamiltonian
7
.
6
.
1
function
1
.
2
|
1
.
2
|
C.
functional
C.
fundamental commutation relations
as an axiom
9
.
1
.
1
orbital angular momentum
3
.
4
.
4
spin
introduction
4
.
5
.
3
C.
|
C.
-factor
9
.
6
Galilean transformation
A.
4
.
3
Gamma
see
|
see
gamma function
C.
gauge transformation
electromagnetic potentials
A.
4
.
10
Gauss' theorem
C.
generalized coordinates
A.
3
.
2
intro
5
.
1
.
10
generator of rotations
5
.
2
geometric phase
A.
37
.
2
Gibbs free energy
8
.
12
microscopic
8
.
13
grad
C.
gradient
C.
grain
7
.
4
.
1
grain boundaries
7
.
4
.
1
Green's function
Laplacian
9
.
5
.
4
ground state
atoms
4
.
9
.
3
free electron gas
7
.
6
.
3
harmonic oscillator
2
.
6
.
4
hydrogen atom
3
.
2
.
3
|
3
.
2
.
4
hydrogen molecular ion
3
.
5
.
7
hydrogen molecule
4
.
2
.
6
|
4
.
5
.
5
|
4
.
6
nonzero energy
2
.
6
.
3
group property
coordinate system rotations
A.
88
Lorentz transform
A.
4
.
8
group theory
5
.
2
group velocity
5
.
5
.
4
intro
5
.
5
.
3
gyromagnetic ratio
9
.
6
C.
|
C.
half-life
excited atoms
5
.
3
.
10
Hamiltonian
2
.
3
and physical symmetry
5
.
2
atoms
4
.
9
.
1
classical
A.
3
.
4
electromagnetic field
9
.
3
free electron gas
7
.
6
.
1
gives time variation
5
.
1
.
1
harmonic oscillator
2
.
6
.
1
partial
2
.
6
.
2
hydrogen atom
3
.
2
.
1
hydrogen molecular ion
3
.
5
.
1
hydrogen molecule
4
.
2
.
1
in matrix form
4
.
8
numbering of eigenfunctions
2
.
3
one-dimensional free space
5
.
5
.
1
relativistic, non quantum
A.
4
.
10
Hamiltonian dynamics
relation to Heisenberg picture
5
.
1
.
10
Hamiltonian perturbation coefficients
10
.
1
.
1
Hankel functions
spherical
A.
48
.
1
harmonic oscillator
2
.
6
classical frequency
2
.
6
eigenfunctions
2
.
6
.
4
eigenvalues
2
.
6
.
3
energy spectrum
2
.
6
.
3
ground state
2
.
6
.
4
Hamiltonian
2
.
6
.
1
partial Hamiltonian
2
.
6
.
2
particle motion
5
.
6
.
4
Hartree product
4
.
7
|
6
.
3
.
1
Hartree-Fock
6
.
3
Coulomb integrals
6
.
3
.
3
exchange integrals
6
.
3
.
3
restricted
closed shell
6
.
3
.
1
open shell
6
.
3
.
1
unrestricted
6
.
3
.
1
C.
heat
8
.
7
Heisenberg
uncertainty principle
2
.
2
uncertainty relationship
3
.
4
.
3
helium ionization energy
10
.
1
.
2
Hellmann-Feynman theorem
10
.
1
.
1
Helmholtz equation
A.
48
.
2
Green's function solution
A.
48
.
2
Helmholtz free energy
8
.
12
microscopic
8
.
13
Hermitian matrices
C.
Hermitian operators
1
.
6
hidden variables
2
.
4
.
2
|
11
.
2
hidden versus nonexisting
3
.
1
.
4
hieroglyph
7
.
10
.
2
|
10
.
1
.
6
.
3
holes
in shells
9
.
1
.
8
Hund's rules
7
.
10
.
2
hybridization
4
.
11
.
4
hydrogen atom
3
.
2
eigenfunctions
3
.
2
.
4
eigenvalues
3
.
2
.
3
energy spectrum
3
.
2
.
3
ground state
3
.
2
.
3
|
3
.
2
.
4
Hamiltonian
3
.
2
.
1
relativistic corrections
10
.
1
.
6
hydrogen bonds
4
.
11
.
3
|
7
.
1
hydrogen molecular ion
3
.
5
bond length
3
.
5
.
7
experimental binding energy
3
.
5
.
7
ground state
3
.
5
.
7
Hamiltonian
3
.
5
.
1
shared states
3
.
5
.
4
hydrogen molecule
4
.
2
binding energy
4
.
2
.
6
bond length
4
.
2
.
6
ground state
4
.
2
.
6
|
4
.
5
.
5
|
4
.
6
Hamiltonian
4
.
2
.
1
hyperfine splitting
10
.
1
.
6
1
.
1
|
1
.
2
|
C.
|
C.
inverse
1
.
1
C.
|
C.
C.
ideal gas
quantum derivation
8
.
14
.
4
thermodynamic properties
8
.
12
ideal gas law
8
.
14
.
4
ideal magnetic dipole
9
.
5
.
2
identical particles
4
.
6
iff
1
.
3
|
C.
imaginary part
1
.
1
impact parameter
A.
48
incompressibility
emph
7
.
6
.
4
index notation
C.
indistinguishable particles
8
.
2
inner product
multiple variables
1
.
7
.
2
inner product of functions
1
.
3
inner product of vectors
1
.
3
insulated system
8
.
10
integer
C.
intelligent designers
A.
73
intensive variable
8
.
7
internal energy
8
.
7
interpretation
interpretations
2
.
4
.
1
many worlds
11
.
5
orthodox
2
.
4
relative state
11
.
4
statistical
2
.
4
inverse
C.
inversion operator
see
parity |
5
.
3
.
7
ionic bonds
4
.
11
.
5
ionic molecules
7
.
2
ionic solids
7
.
2
ionization
3
.
2
.
3
ionization energy
7
.
2
atoms
4
.
9
.
4
Hartree-Fock
6
.
3
.
5
.
1
helium
10
.
1
.
2
hydrogen atom
3
.
2
.
3
iso
C.
isolated
C.
isolated system
8
.
10
C.
|
C.
K
C.
C.
|
C.
kappa
see
C.
ket
1
.
3
|
C.
ket notation
spherical harmonics
3
.
1
.
3
spin states
4
.
4
kinetic energy
operator
2
.
3
kinetic energy operator
in spherical coordinates
3
.
2
.
1
Klein-Gordon equation
9
.
2
kmol
C.
Koopman's theorem
6
.
3
.
5
.
1
Kramers relation
A.
102
L
C.
C.
C.
|
C.
C.
ladder operators
angular momentum
9
.
1
.
2
Lagrangian
relativistic
A.
4
.
10
simplest case
A.
3
.
1
Lagrangian mechanics
A.
3
Lagrangian multipliers
derivations
A.
50
for variational statements
6
.
1
.
3
Lamb shift
10
.
1
.
6
|
10
.
1
.
6
.
3
lambda
see
Landé
-factor
10
.
1
.
6
.
2
Laplace equation
A.
93
.
2
Laplacian
C.
Larmor frequency
definition
9
.
8
.
2
Larmor precession
9
.
8
.
3
laser
5
.
3
.
2
latent heat of vaporization
8
.
12
lattice
7
.
2
basis
7
.
2
diamond
7
.
5
lithium
7
.
4
.
1
NaCl
7
.
2
bcc
7
.
4
.
1
|
7
.
4
.
1
diamond
7
.
5
fcc
7
.
2
lithium
7
.
4
.
1
NaCl
7
.
2
one-dimensional
7
.
4
.
2
primitive translation vector
7
.
4
.
5
reciprocal
lithium
7
.
4
.
11
NaCl
7
.
4
.
11
one-dimensional
7
.
4
.
7
primitive vectors
7
.
4
.
11
three-dimensional
7
.
4
.
11
three-dimensional
primitive vectors
7
.
4
.
11
unit cell
7
.
2
bcc
7
.
4
.
1
fcc
7
.
2
law of Dulong and Petit
7
.
10
.
1
Lebesgue integration
A.
43
length of a vector
1
.
3
Lennard-Jones potential
7
.
1
Casimir-Polder
7
.
1
lifetime
excited atom
5
.
3
.
10
light waves
classical
9
.
4
light-cone
see
special relativity
C.
linear combination
C.
linear momentum
classical
2
.
2
eigenfunctions
5
.
4
.
2
eigenvalues
5
.
4
.
2
operator
2
.
3
symmetry and conservation
5
.
2
localization
absence of
5
.
5
.
2
London forces
7
.
1
Casimir-Polder
7
.
1
Lorentz factor
A.
4
.
2
Lorentz transformation
see
special relativity
Lorentz-Fitzgerald
see
special relativity
luminosity
A.
48
Lyman transitions
3
.
2
.
3
M
C.
C.
C.
C.
C.
C.
Madelung constant
7
.
2
magnetic dipole moment
9
.
6
magnetic dipole transitions
Hamiltonian
A.
40
intro
5
.
3
.
5
selection rules
see
selection rules
magnetic quantum number
3
.
1
.
2
magnetic spin anomaly
9
.
6
magnetic vector potential
classical derivation
A.
93
.
7
in the Dirac equation
A.
95
quantum derivation
9
.
3
relativistic derivation
A.
4
.
10
magnitude
1
.
1
maser
ammonia
4
.
3
mass-energy relation
see
special relativity
Dirac equation
emph
9
.
2
fine-structure
emph
10
.
1
.
6
.
1
need for quantum field theory
10
.
2
matching regions
A.
47
mathematicians
A.
4
.
7
|
A.
58
matrix
1
.
4
|
C.
maximum principle
Laplace equation
A.
93
.
2
Maxwell relations
8
.
12
Maxwell's equations
9
.
4
Maxwell-Boltzmann distribution
7
.
9
canonical probability
8
.
5
for given energy
8
.
4
mean value property
Laplace equation
A.
93
.
2
measurable values
2
.
4
.
1
measurement
2
.
4
.
1
meson
4
.
4
metals
7
.
4
method of stationary phase
A.
44
metric prefixes
C.
mole
8
.
7
molecular mass
8
.
7
molecular solids
7
.
1
molecules
ionic
7
.
2
momentum space wave function
5
.
4
.
2
moving mass
seespecial relativity
A.
4
.
2
mu
see
multipole expansion
9
.
5
.
3
N
C.
C.
C.
nabla
C.
natural
C.
nearly free electron model
7
.
8
Neumann functions
spherical
A.
48
.
1
Newton's second law
in quantum mechanics
5
.
1
.
8
Newtonian analogy
2
.
3
Maxwellian analogy
10
.
2
.
3
.
2
Newtonian mechanics
2
.
1
in quantum mechanics
5
.
1
.
8
noble gas
4
.
9
.
3
noncanonical Hartree-Fock equations
A.
58
nonexisting versus hidden
3
.
1
.
4
nonholonomic
A.
37
.
2
norm of a function
1
.
3
normal
C.
normalized
1
.
3
normalized wave functions
2
.
1
nu
see
nuclear magnetic resonance
9
.
8
nuclear magneton
9
.
6
observable values
2
.
4
.
1
occupation numbers
single-state
10
.
2
.
1
omega
see
one-dimensional free space
Hamiltonian
5
.
5
.
1
operator
exponential of an operator
5
.
1
.
10
operators
1
.
4
angular momentum component
3
.
1
.
2
Hamiltonian
2
.
3
kinetic energy
2
.
3
in spherical coordinates
3
.
2
.
1
linear momentum
2
.
3
position
2
.
3
potential energy
2
.
3
quantum mechanics
2
.
3
square angular momentum
3
.
1
.
3
total energy
2
.
3
orbitals
6
.
3
.
1
orthodox interpretation
2
.
4
orthogonal
1
.
3
orthonormal
1
.
3
C.
p states
3
.
2
.
4
C.
p-state
C.
parity
5
.
3
.
7
as a symmetry
5
.
2
conservation in atomic transitions
5
.
3
.
7
inversion operator
5
.
3
.
7
multiplies instead of adds
5
.
3
.
7
orbital angular momentum
5
.
3
.
7
spherical harmonics
derivation
A.
15
symmetry and conservation
5
.
2
intro
5
.
3
.
7
|
5
.
3
.
7
Parseval's relation
A.
43
partial wave analysis
A.
48
.
1
partition function
8
.
5
Paschen transitions
3
.
2
.
3
Pasternack relation
A.
102
Pauli exclusion principle
4
.
7
atoms
4
.
9
.
4
common phrasing
4
.
9
.
4
free electron gas
7
.
6
Pauli repulsion
4
.
10
Pauli spin matrices
9
.
1
.
9
generalized
9
.
1
.
10
periodic table
4
.
9
.
4
full
4
.
9
.
6
periodic zone scheme
7
.
7
.
2
permanents
4
.
7
permittivity of space
3
.
2
.
1
perpendicular bisector
C.
perturbation theory
helium ionization energy
10
.
1
.
2
second order
10
.
1
.
1
time dependent
5
.
3
.
8
time-independent
10
.
1
weak lattice potential
7
.
8
.
1
phase angle
C.
phase equilibrium
8
.
12
phase speed
5
.
5
.
2
Phi
see
|
see
,
phonons
7
.
10
.
1
photon
3
.
2
.
3
|
C.
energy
3
.
2
.
3
spin value
4
.
4
photon packet
10
.
2
.
3
.
2
physical symmetry
commutes with Hamiltonian
5
.
2
physicists
2
.
4
.
1
|
2
.
4
.
2
|
5
.
1
.
9
|
5
.
3
.
4
|
5
.
3
.
9
|
6
.
2
.
3
|
6
.
3
.
5
.
4
|
7
.
4
.
5
|
7
.
4
.
11
|
7
.
10
.
2
|
9
.
4
|
9
.
5
|
9
.
6
|
9
.
6
|
10
.
2
.
1
|
10
.
2
.
3
.
2
|
A.
4
.
5
|
A.
4
.
6
|
A.
4
.
6
|
A.
4
.
7
|
A.
15
|
A.
48
|
A.
48
|
A.
48
|
A.
48
.
1
|
A.
60
pi
see
pi bonds
4
.
11
.
2
Plancherel's theorem
A.
43
Planck's blackbody spectrum
8
.
14
.
5
Planck's constant
2
.
3
Planck-Einstein relation
3
.
2
.
3
point charge
static
9
.
5
.
1
pointer states
3
.
2
.
4
Poisson bracket
5
.
1
.
10
Poisson equation
9
.
5
.
4
polar bonds
4
.
11
.
3
poly-crystalline
7
.
4
.
1
population inversion
5
.
3
.
2
position
eigenfunctions
5
.
4
.
1
eigenvalues
5
.
4
.
1
operator
2
.
3
possible values
2
.
4
.
1
potential
existence
A.
93
.
1
potential energy
operator
2
.
3
potential energy surfaces
6
.
2
.
3
Poynting vector
10
.
2
.
3
.
1
prefixes
YZEPTGMkmunpfazy
C.
pressure
8
.
7
primitive cell
7
.
4
.
11
primitive translation vector
one-dimensional
7
.
4
.
5
reciprocal lattice
7
.
4
.
11
three-dimensional
7
.
4
.
11
principal quantum number
3
.
2
.
2
principle of relativity
A.
4
.
2
probabilities
evaluating
2
.
6
.
6
from coefficients
2
.
4
.
2
probability current
A.
49
probability density
4
.
2
.
3
probability to find the particle
2
.
1
promotion
4
.
11
.
4
proper distance
see
special relativity
proper time
see
special relativity
Psi
see
|
see
pure substance
8
.
C.
Pythagorean theorem
A.
4
.
4
C.
C.
quantum confinement
2
.
5
.
9
|
7
.
6
.
5
quantum dot
2
.
5
.
9
quantum electrodynamics
electron g factor
9
.
6
Feynman's book
10
.
2
photon exchange
intro
5
.
1
.
5
quantum interference
intro
2
.
1
quantum mechanics
acceleration
5
.
1
.
8
force
5
.
1
.
8
Newton's second law
5
.
1
.
8
Newtonian mechanics
5
.
1
.
8
velocity
5
.
1
.
8
quantum well
2
.
5
.
9
quantum wire
2
.
5
.
9
quark
spin
4
.
4
quarks
Dirac equation
9
.
2
proton and neutron
9
.
6
C.
C.
|
C.
C.
Rabi flopping frequency
9
.
8
.
4
radiation
emission and absorption
5
.
3
random number generator
2
.
4
.
2
Rayleigh formula
partial wave expansion
A.
48
.
1
spherical Bessel functions
A.
48
.
1
real part
1
.
1
reciprocal lattice
see
lattice, reciprocal
reduced zone scheme
7
.
7
.
2
reflection coefficient
5
.
9
|
5
.
9
|
A.
49
relative state formulation
11
.
5
relative state interpretation
11
.
4
relativistic corrections
hydrogen atom
10
.
1
.
6
Relativistic effects
Dirac equation
9
.
2
relativistic mass
seespecial relativity
A.
4
.
2
relativity
see
special relativity |
C.
resonance factor
9
.
8
.
4
rest mass
seespecial relativity
A.
4
.
2
restricted Hartree-Fock
6
.
3
.
1
reversibility
8
.
9
RHF
6
.
3
.
1
rho
see
rot
C.
C.
s state
C.
s states
3
.
2
.
4
C.
saturated
8
.
12
scalar
C.
scattering
5
.
8
one-dimensional coefficients
5
.
9
three-dimensional coefficients
A.
48
scattering amplitude
A.
48
Schrödinger equation
5
.
1
failure?
11
.
4
integral form
A.
48
.
2
Schrödinger’s cat
11
.
1
second law of thermodynamics
8
.
8
second quantization
10
.
2
.
3
.
2
selection rules
angular momentum conservation
5
.
3
.
6
derivation
A.
40
electric dipole transitions
5
.
3
.
5
electric quadrupole transitions
5
.
3
.
5
magnetic dipole transitions
5
.
3
.
5
parity conservation
5
.
3
.
7
self-adjoint
C.
self-consistent field method
6
.
3
.
4
semi-conductors
band gap
7
.
5
conduction
7
.
3
lattice
see
lattice, diamond
manipulation
7
.
3
separation of variables
2
.
6
.
2
for atoms
4
.
9
.
2
for free electron gas
7
.
6
.
2
linear momentum
5
.
4
.
2
position
5
.
4
.
1
shielding approximation
4
.
9
.
2
SI prefixes
C.
sigma
see
sigma bonds
4
.
11
.
1
simple cubic lattice
7
.
7
.
1
sin
C.
singlet state
4
.
5
.
6
derivation
9
.
1
.
5
skew-Hermitian
C.
Slater determinants
4
.
7
small perturbation theory
7
.
8
.
1
solid angle
C.
solids
7
.
band structure
intro
7
.
3
covalent
7
.
5
ionic
7
.
2
molecular
7
.
1
sp
hybridization
4
.
11
.
4
space-like
see
special relativity
space-time
see
special relativity
space-time interval
see
special relativity
special relativity
A.
4
action
A.
4
.
10
canonical momentum
A.
4
.
10
causality and proper time
A.
4
.
5
four-vectors
A.
4
.
6
dot product
A.
4
.
6
in terms of momentum
A.
4
.
2
light-cone
A.
4
.
5
Lorentz force
A.
4
.
10
derivation
A.
4
.
10
.
1
Lorentz transformation
A.
4
.
3
basic derivation
A.
4
.
3
.
1
group derivation
A.
4
.
8
.
1
group property
A.
4
.
8
index notation
A.
4
.
7
Lorentz-Fitzgerald contraction
A.
4
.
2
derivation
A.
4
.
3
.
1
mass-energy relation
A.
4
.
2
derivation
A.
4
.
9
Lagrangian derivation
A.
4
.
10
mechanics
intro
A.
4
.
9
Lagrangian
A.
4
.
10
momentum four-vector
A.
4
.
9
moving mass
A.
4
.
2
derivation
A.
4
.
9
Lagrangian derivation
A.
4
.
10
proper distance
A.
4
.
4
as dot product
A.
4
.
6
proper time
A.
4
.
4
relativistic mass
A.
4
.
2
rest mass energy
A.
4
.
2
derivation
A.
4
.
9
space-like
A.
4
.
4
space-time
A.
4
.
6
space-time interval
A.
4
.
4
causality
A.
4
.
5
superluminal interaction
A.
4
.
5
time dilation
derivation
A.
4
.
3
.
1
time-dilation
A.
4
.
2
time-like
A.
4
.
4
velocity transformation
A.
4
.
3
derivation
A.
4
.
3
.
1
warp factor
A.
4
.
5
specific heat
constant pressure
8
.
7
constant volume
8
.
7
values
7
.
10
.
1
specific volume
8
.
7
molar
8
.
7
spectral line broadening
5
.
3
.
8
spectrum
hydrogen
3
.
2
.
3
spherical Bessel functions
A.
48
.
1
spherical coordinates
3
.
1
.
2
spherical Hankel functions
A.
48
.
1
spherical harmonics
derivation
A.
80
derivation from the ODE
A.
15
derivation using ladders
A.
80
generic expression
A.
15
intro
3
.
1
.
3
Laplace equation derivation
A.
15
parity
A.
15
spherical Neumann functions
A.
48
.
1
spin
4
.
4
fundamental commutation relations
introduction
4
.
5
.
3
value
4
.
4
- and
-eigenstates
9
.
1
.
9
spin down
4
.
4
spin orbitals
6
.
3
.
1
spin states
ambiguity in sign
A.
87
axis rotation
A.
87
spin up
4
.
4
spinor
4
.
5
.
1
spontaneous emission
quantum derivation
10
.
2
.
4
spontaneous emission rate
5
.
3
.
9
standard deviation
3
.
3
definition
3
.
3
.
1
simplified expression
3
.
3
.
3
Stark effect
10
.
1
.
5
stationary states
5
.
1
.
4
statistical interpretation
2
.
4
statistical mechanics
7
.
9
statistics
bosons
7
.
9
fermions
7
.
9
Stefan-Boltzmann formula
8
.
14
.
5
Stefan-Boltzmann law
8
.
14
.
5
Stern-Gerlach apparatus
9
.
7
stoichiometric coefficient
8
.
12
Stokes' theorem
C.
superfluidity
Bose-Einstein condensation
7
.
9
superluminal interaction
Bell's theorem
11
.
2
hidden variables
11
.
2
many worlds interpretation
11
.
5
quantum
2
.
1
do not allow communication
11
.
2
produce paradoxes
11
.
2
relativistic paradoxes
A.
4
.
5
symmetrization requirement
graphical depiction
8
.
2
identical bosons
4
.
6
identical fermions
see
antisymmetrization
indistinguishable particles
8
.
2
using groupings
4
.
7
using occupation numbers
10
.
2
.
1
using permanents
4
.
7
symmetry
C.
C.
|
C.
tau
see
temperature
8
.
1
|
C.
definition
8
.
4
Carnot
8
.
9
definition using entropy
8
.
12
temperatures above absolute zero
7
.
9
thermal de Broglie wavelength
8
.
14
thermal efficiency
8
.
9
thermal equilibrium
8
.
thermodynamics
first law
8
.
7
second law
8
.
8
third law
8
.
10
Theta
see
|
see
,
third law of thermodynamics
8
.
10
throw the dice
2
.
4
.
2
time
directionality
11
.
6
time dependent perturbation theory
5
.
3
.
8
time variation
Hamiltonian
5
.
1
.
1
time-dilation
see
special relativity
time-like
see
special relativity
total energy
operator
2
.
3
transition probability
5
.
3
.
8
transition rate
5
.
3
.
9
transitions
hydrogen atom
3
.
2
.
3
transmission coefficient
5
.
9
|
5
.
9
|
A.
49
transpose of a matrix
C.
triangle inequality
5
.
3
.
6
triple product
C.
triplet states
4
.
5
.
6
derivation
9
.
1
.
5
tunneling
5
.
8
.
2
Stark effect
10
.
1
.
5
WKB approximation
5
.
9
turning point
5
.
6
.
3
turning points
WKB approximation
5
.
7
twilight terms
4
.
3
exchange terms
4
.
3
Hartree-Fock
6
.
3
.
3
Lennard-Jones/London force
A.
61
lithium hydride
4
.
3
particle exchange rate
5
.
1
.
5
spontaneous emission
10
.
2
.
4
two state systems
ground state energy
4
.
3
time variation
5
.
1
.
5
unsteady perturbations
5
.
3
two-state systems
atom-photon model
10
.
2
.
4
u
C.
C.
UHF
6
.
3
.
1
uncertainty principle
angular momentum
3
.
1
.
4
energy
2
.
6
.
4
|
5
.
1
.
4
Heisenberg
2
.
2
position and linear momentum
2
.
2
uncertainty relationship
generalized
3
.
4
.
2
Heisenberg
3
.
4
.
3
unit cell
seelattice
7
.
2
unit matrix
C.
unitary
matrix
A.
58
time advance operator
5
.
1
.
10
unitary operators
C.
universal gas constant
7
.
10
.
1
|
8
.
12
unrestricted Hartree-Fock
6
.
3
.
1
C.
|
C.
C.
vacuum energy
5
.
3
.
10
vacuum state
10
.
2
.
1
valence band
7
.
3
values
measurable
2
.
4
.
1
observable
2
.
4
.
1
possible
2
.
4
.
1
Van der Waals forces
7
.
1
Casimir-Polder
7
.
1
variational method
3
.
5
.
6
helium ionization energy
10
.
1
.
2
hydrogen molecular ion
3
.
5
.
6
hydrogen molecule
4
.
2
.
5
variational principle
6
.
1
basic statement
6
.
1
.
1
differential form
6
.
1
.
2
Lagrangian multipliers
6
.
1
.
3
vector
1
.
2
|
C.
vectorial product
C.
velocity
in quantum mechanics
5
.
1
.
8
vibronic coupling terms
A.
53
virial theorem
5
.
1
.
7
virtual work
A.
3
.
3
viscosity
8
.
9
C.
|
C.
C.
warp factor
see
special relativity
wave function
2
.
1
multiple particles
4
.
1
multiple particles with spin
4
.
5
.
4
with spin
4
.
5
.
1
wave number
5
.
5
.
4
Floquet
7
.
4
.
5
Fourier versus Floquet
7
.
4
.
7
free electron gas
7
.
6
.
2
simple
1
.
5
wave number vector
Bloch function
7
.
4
.
11
wave packet
accelerated motion
5
.
6
.
2
definition
5
.
5
.
3
free space
5
.
5
|
5
.
6
.
1
harmonic oscillator
5
.
6
.
4
partial reflection
5
.
8
.
1
physical interpretation
5
.
5
.
3
reflection
5
.
6
.
3
weak force
boson exchange
intro
5
.
1
.
5
Wigner-Seitz cell
7
.
4
.
11
WKB approximation
connection formulae
A.
47
WKB connection formulae
A.
47
WKB theory
5
.
7
Wronskian
A.
49
C.
|
C.
X-ray diffraction
7
.
10
.
3
xi
see
C.
|
C.
C.
C.
|
C.
Zeeman effect
10
.
1
.
4
intermediate
10
.
1
.
6
.
2
weak
10
.
1
.
6
.
2
zero matrix
C.
zero point energy
6
.
2
.
3
zeroth law of thermodynamics
8
.
1
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C
hybridization
| see
,
-factor
| see
-factor
| see ,
| see
hybridization
- and 
-eigenstates
| see ,
