Display Parameters
Show Background Animation
Text Colors
Basic Blue
Static Spectral Colors
Rotating Spectral Colors
Return
Comparison of Quantum Mechanics Texts
Outline & Cross-reference
Text: Quantum Theory in the Computer Age
Detailed Text Listing
Unit 1.
Introduction to Quantum Amplitudes
Unit 2.
Introduction to Wave Dynamics
Unit 3.
Introduction to Fourier Analysis and Symmetry
Unit 4.
Introduction to Wave Equations
Unit 5.
Introduction to Periodic Potentials and Symmetry
Unit 6.
Introduction to Time-Variable Perturbations and Transitions
Unit 7.
Quantum Harmonic Oscillators
Unit 8.
Quantum Rotation and Angular Momentum
Unit 9.
Quantum Orbitals and Central force dynamics (In preparation)
Unit 10.
Multiparticle States and Interactions (In preparation)
Unit 11.
Polyatomic Molecules (In preparation)
Unit 12.
Relativistic Spin and Symmetry (Proposed)
Unit 13.
Relativistic Quantum Field Theory (Proposed)
Text: Principles of Symmetry, Dynamics, and Spectroscopy
Title & Preface
Chapter 1.
A Review of Matrix Algebra and Quantum Mechanics
Chapter 2.
Basic Theory and Applications of Symmetry Representations (Abelian Symmetry Groups)
Chapter 3.
Basic Theory and Applications of Symmetry Representations (Non-Abelian Symmetry Groups)
Chapter 4.
Theory and Applications of Higher Finite Symmetry and Induced Representations
Chapter 5.
Representations of Continuous Rotation Groups and Applications
Chapter 6.
Theory and Applications of Symmetry Representation Products (Finite Groups)
Chapter 7.
Theory and Applications of Symmetry Representation Products (Continuous Rotation Groups)
Chapter 8.
Symmetry Analysis for Semiclassical and Quantum Mechanics: Dynamics with High Quanta
Appendix F.
Formulas and Tables of Group Representations and Related Quantities
Appendix G.
Schur's Lemma and Irreducible Representations and Orthogonality
Index.
PSDS Index and PSDS⇔CTCA Page⇔Chapter/Section Cross-Reference Strips
2018 Lecture Topics
2018 Detailed Lecture Listing
2014 Info Page
Lecture 1.
Spectral hierarchy of Born-Openheimer approximations to AMOP
(1.16.18)
,
, Video
Lecture 2.
Symmetry group representations and AMOP Hamiltonian matrices
(1.19.18)
,
, Video
Lecture 3.
Symmetry group 𝒢 representations and AMOP Hamiltonian
H
(or
K
) matrices,
𝒟
(α)
irreps, Ψ
(α)
wave functions, and eigensolution projectors
P
(α)
I.
𝒢 = C
2
, C
3
, C
6
= Cyclic groups of order 2, 3, 6
(1.22.18)
,
, Video
Lecture 4.
Symmetry group 𝒢 representations and AMOP Hamiltonian
H
(or
K
) matrices,
𝒟
(α)
irreps, Ψ
(α)
wave functions, and eigensolution projectors
P
(α)
II.
𝒢 = U(2) = Unitary group of dimension 2
(1.24.18)
,
, Video
Lecture 5.
Symmetry group 𝒢 representations and AMOP Hamiltonian
H
(or
K
) matrices,
𝒟
(α)
irreps, Ψ
(α)
wave functions, eigensolutions I.
𝒢 = U(2), spin-½ irreps: Euler
R
(
α
β
γ
)
vs Darboux
R
[
ϕϑΘ
]
rotations and applications
(1.29.18)
,
, Video
Lecture 6.
Symmetry group 𝒢 representations and AMOP Hamiltonian
H
(or
K
) matrices,
𝒟
(α)
irreps, Ψ
(α)
wave functions, eigensolutions II.
(1.31.18)
,
, Video
Lecture 7.
Symmetry group 𝒢 = U(1) representations and 1D HO Hamiltonian
H
= ħω
a
†
a
operators,
1D HO wave eigenfunctions Ψ
n
, and coherent α-states
(2.5.18)
,
, Video
Lecture 8.
Symmetry group 𝒢 = U(2) representations and 2D HO Hamiltonian
H
= ħω
ab
a
a
†
a
b
operators,
2D HO wave eigenfunctions Ψ
n,m
, and coherent [
α
]-states
(2.7.18)
,
, Video
Lecture 9.
Wigner D
J
mn
irreps of U(2)~R(3) give atomic and molecular eigenfunctions Ψ
m,n
of
3D rotor Hamiltonian
H
=
A
J
x
2
+
B
J
y
2
+
C
J
z
2
and
angular momentum uncertainty effects.
(2.12.18)
,
, Video
Lecture 10.
Rotational Energy Surfaces (RES) and Lab vs Body molecular rotor states, levels, and spectra - I.:
Body symmetry R(2) of prolate & oblate rotors vs. D
2
of asymmetric rotor
H
=
A
J
x
2
+
B
J
y
2
+
C
J
z
2
(2.14.18)
,
, Video
Lecture 11.
Rotational Energy Surfaces (RES) and Lab vs Body molecular rotor states, levels, and spectra I:
Body symmetry
O
of octahedral rotors
H=
B
J
2
+Σt
kq
T
q
k
(2.21.18)
,
, Video
Lecture 12.
Discrete symmetry subgroups of O(3) and application to tunneling and vibrational dynamics:
D
3
and C
3v
group products, classes, and irrep projection operators
(2.21.18)
,
, Video
Lecture 13.
Discrete symmetry subgroups of O(3) using Mock-Mach principle:
D
3
and C
3v
Lab vs. Body group and projection operator formulation of ortho-complete eigensolutions
(2.26.18)
,
, Video
Lecture 14.
Discrete symmetry subgroups of O(3) using Mock-Mach principle:D
3
~ C
3v
LAB vs. BOD
Vibrational eigensolutions, D
6
~C
6v
bands, subgroup correlation, and Frobenius reciprocity
(3.2.18)
,
, Video
Lecture 15.
Discrete symmetry subgroups of O(3)⊃(Octahedral O
h
⊃O~T
d
, Cubic-Tetrahedral T
h
⊃T):
Characters and subgroup-chain defined ireps, and applications to SF
6
and CF
4
spectra
(3.5.18)
,
, Video
Lecture 16.
Discrete symmetry subgroups of O(3)⊃(Octahedral
O
h
⊃
O
): Deriving D(α)-matrices defined by
subgroup-chains
O
⊃
D
4
⊃
C
4
,
O
⊃
D
4
⊃
D
2
, and O⊃
D
3
⊃
C
3
applications to IR spectra of SF
6
(3.7.18)
,
, Video
Lecture 17.
Discrete symmetry subgroups of O(3)⊃(Octahedral
O
h
⊃
O
): Part II Full D(α)-matrices defined
by subgroup-chains O⊃D
4
⊃C
4
, D
2
, or C
3
applied to eigensolutions of O
h
-tensors
>T
[4]
+T
[6]
(3.12.18)
,
, Video
Lecture 18.
U(2)~O(3)⊃Oh Clebsch-Gordan irep product analysis, spin-orbit multiplets, and Wigner tensor
matrices giving exact orbital splitting for O(3)⊃Oh symmetry breaking
(3.26.18)
,
, Video
Lecture 19.
S
1
⊂S
2
⊂S
3
⊂S
4
⊂S
5
... permutation symmetry algebra and spinor-rotor correlations
(3.28.18)
,
, Video
Lecture 20.
Interwining (S
1
⊂S
2
⊂S
3
⊂S
4
⊂S
5
...)*(U(1)⊂U(2)⊂U(3)⊂U(4)⊂U(5) ...) algebras
and tensor operator applications to spinor-rotor or orbital correlations
(4.2.18)
,
, Video
Lecture 21.
Characters of intertwining (S
n
)*(U(m)) algebras and quantum applications
(4.4.18)
,
, Video
Lecture 22.
Atomic shell models using intertwining (S
n
)*(U(m)) matrix operators
(4.9.18)
,
, Video
Lecture 23.
(S
n
)*(U(m)) shell model of electrostatic quadrupole-quadrupole-e interactions
(4.16.18)
,
, Video
Lecture 24.
(S
n
)*(U(m)) shell model of electronic spin-orbit states and interactions
(4.18.18)
,
, Video
Lecture 25.
(S
3
)*(U(3)) ⊂ U(6) models of p
3
electronic spin-orbit states and couplings I.
(4.23.18)
,
, Video
Lecture 26.
(S
3
)*(U(3)) ⊂ U(6) models of p
3
electronic spin-orbit states and couplings II.
(4.25.18)
,
, Video
Lecture 27.
Molecular rovibrational spectra : O
h
symmetry, SF
6
and. UF
6
examples
(4.30.18)
,
, Video
Lecture 28.
Symmetry spin species for C
2
, CH
4
, SF
6
, and molecular energy surfaces:
Born-Oppenheimer-Adiabadicity: How BOA works until it doesn’t
(5.2.18)
,
, Video
Lecture 29.
From CH
4
to SF
6
to C
60
: a study in spectacular spectral contrasts
(5.8.18)
,
, Video
Listing of Other Classes
2012 PHYS 3614 Modern Physics
2013 PHYS 5093 Group Theory in Quantum Mechanics
2013 PHYS 5103 Advanced Mechanics
2014 PHYS 5513 Atomic, Molecular, and Optical Physics
2014 PHYS 5103 Advanced Mechanics
2015 PHYS 5093 Group Theory in Quantum Mechanics
2016 PHYS 3922H Honors Colloquium
2016 PHYS 5103 Advanced Mechanics
2017 PHYS 5093 Group Theory in Quantum Mechanics
2017 PHYS 5103 Advanced Mechanics
Related Papers & Talks
Frame transformation relations and multipole transitions in symmetric polyatomic molecules - RMP 1978
Rovibrational Spectral Fine Structure of Icosahedral Molecules - CPL 1986
Relativity Lecture (Unit_2) - Harvard 2010
Symmetry Eigensolutions on the Cheap - OAI 2010
Weapons of Math Instruction - INBRE Workshop 2012
➪ Molecular Eigensolution Symmetry Analysis and Fine Structure - IJMS 1/4/2013
Molecules and Molecular Spectroscopy - UA ModPhys 3/25/2013
Quantum Revivals of Morse Oscillators and Farey-Ford Geometry - 2013
Special Relativity and Quantum Theory by Ruler and Compass - AJP 2014 (Pre-Print)
ResearchGate Contibutions Page - W.G. Harter
Presentation on: Molecules and Molecular Spectroscopy - UAF 12/17/2017
"Learning about molecules from Quantum theory and Learning about Quantum theory from molecules"
International Symposium on Molecular Spectroscopy - Columbus 2012
RelaWavity Drafts
Special Relativity and Quantum Theory by Ruler and Compass - Current Expanded-Earlier draft
Relawavity: A simple way to introduce relativity and quantum theory using ruler & compass geometry
Draft UAF 2017
Current draft via Apple Pages
Current draft via TeX with reference linking
What Einstein left out: Gaining clarity in modern physics curricula
, Draft UAF 2017
Prototype draft via Apple Pages
Latest draft via TeX with reference linking
LearnIt - Physics Web Applications
Comprehensive Listing of Harter-Soft Web Resources for Physics
