Short physical chemistry lecture on an example of the superposition principle.

For a linear combination of eigenfunctions of the Hamiltonian, the probability of measuring each energy eigenvalue is proportional to its coefficient squared. The expectation value, or average value, of the energy is a weighted average of all energy values where the coefficients squared are the weights.

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1. Introduction
2. Blackbody Radiation
3. Photoelectric Effect
4. Rydberg Formula
5. Bohr Hydrogen Model 1: Radius
6. Bohr Hydrogen Model 2: Energy
7. Wave-Particle Duality
8. Heisenberg Uncertainty Principle in Measurement
9. Classical Wave Equation
10. Vibrating String
11. Vibrating String Animation
12. Schrodinger Equation "Derivation"
13. Operators
14. Eigenvalues and Eigenfunctions
15. Interpreting the Wavefunction
16. Particle in a Box
17. Normalization
18. Particle in a Box Wavefunction Plots
19. UV-Vis Spectra of Polyenes
20. Average Position
21. Average Momentum
22. 3-D Particle in a Box
23. Degeneracy
24. Postulates of Quantum Mechanics 1: Wavefunction
25. Postulates of Quantum Mechanics 2: Operators
26. Postulates of Quantum Mechanics 3: Measurement
27. Postulates of Quantum Mechanics 4: Expectation Values
28. Postulates of Quantum Mechanics 5: Schrodinger Equation
29. Commutators
30. Hermitian Operators
31. Dirac Notation
32. Orthogonality
33. Superposition Principle 1: Basis Sets
34. Superposition Principle 2: Expectation Values
35. Superposition Principle 3: Example
36. Commuting Operators
37. Time Dependence
38. Time Dependence Animation
39. Wavefunction Collapse
40. Schrodinger's Cat
41. Correspondence Principle
42. Harmonic Oscillator Model
43. Classical Harmonic Oscillator 1: Trajectory
44. Classical Harmonic Oscillator 2: Energy
45. Reduced Mass
46. Harmonic Oscillator Energy Levels
47. Diatomic Infrared Spectra
48. Anharmonicity and Overtones
49. Harmonic Oscillator Wavefunctions
50. Even and Odd Functions
51. Harmonic Oscillator Even and Odd Functions
52. 3-D Harmonic Oscillator
53. Polyatomic Molecular Vibrations
54. Rigid Rotor Model
55. Rotation Operators
56. Rigid Rotor Energy Levels
57. Diatomic Microwave Spectra
58. Rovibrational Energy Levels
59. Diatomic Rovibrational Spectra
60. Microwave Spectroscopy Example
61. Rotation-Vibration Interaction
62. Centrifugal Distortion
63. Rigid Rotor Wavefunctions
64. Orthonormality of Spherical Harmonics
65. Angular Momentum Eigenvalues
66. Hydrogen Atom Model
67. Hydrogen Atom Energy Levels
68. Hydrogen Atom Radial Wavefunctions
69. Hydrogen Atom Total Wavefunctions
70. Hydrogen Atomic Orbital Nodes
71. Hydrogen Orbital Eigenvalues
72. Hydrogen Atom Radius
73. Hydrogen Atom Radial Wavefunction Animation
74. Virial Theorem
75. Zeeman Effect
76. Electron Spin
77. Spin-Orbit Coupling
78. Hydrogen Atom Term Symbols
79. Hydrogen Atom Spectrum
80. Helium Atom Hamiltonian
81. Variational Principle
82. Variational Principle Example
83. Linear Variational Method
84. Secular Determinant
85. Linear Variational Example
86. Perturbation Theory
87. Perturbation Theory Derivation
88. Perturbation Theory Example
89. Atomic Units
90. Helium Atom Energy Approximations
91. Hartree-Fock Helium Atom
92. Hartree-Fock Helium Energy
93. Antisymmetry Principle
94. Slater Determinants
95. Hartreee-Fock Atomic Energy
96. Hartree-Fock Operators
97. Hartree-Fock-Roothaan Equations
98. Hartee-Fock Spin
99. Post Hartree-Fock Methods
100. Atomic Electron Configurations
101. Electron Configuration Exceptions
102. Atomic Term Symbols
103. Term Symbols Example 1
104. Term Symbols Example 2
105. Term Symbols Example 3
106. Hund's Rules
107. Atomic Spectra
108. Hydrogen Molecule Hamiltonian
109. Born-Oppenheimer Approximation
110. Hydrogen Molecule-Ion 1: Energy
111. Hydrogen Molecule-Ion 2: Orbitals
112. Molecular Orbital Angular Momentum
113. Molecular Orbital Inversion Symmetry
114. Hydrogen Molecular Orbital Diagram
115. LCAO-MO Theory
116. Diatomic Molecular Orbital Diagrams
117. Bond Order
118. Diatomic Term Symbols
119. Total Wavefunction Symmetry
120. sp Hybridization
121. sp2 Hybridization
122. sp3 Hybridization
123. Lone Pair Hybridization
124. Walsh Diagrams
125. Huckel Theory
126. Pi Resonance
127. Aromaticity
128. Symmetry Websites
129. Symmetry Operations
130. Symmetry Elements
131. Groups
132. Point Groups
133. Point Group Examples
134. Point Group Flow Chart
135. Group Multiplication Tables
136. Symmetry Operator Matrices
137. Irreducible Representations
138. Character Tables 1
139. Character Tables 2
140. Determining Irreps
141. Generating Operators
142. Group Theory Example
143. Nuclear Spin
144. Magnetic Moments
145. Nuclear Magnetic Resonance
146. NMR Spectrometer
147. Magnetic Shielding
148. Chemical Shift
149. Spin-Spin Coupling
150. First Order Spectra
151. Chemical Equivalence
152. The n+1 Rule
153. Second Order Spectra
154. Particle in a Ring Model
155. Particle in a Ring Energies
156. Particle in a Ring Wavefunctions
157. Huckel's Rule
158. UV-Vis Spectrum of Aromatics
159. Particle in a Ring Eigenvalues

Physical chemistry microlectures covering the topics of an undergraduate physical chemistry course on quantum chemistry and spectroscopy. Topics include the need for quantum theory, the classical wave equation, the principles of quantum mechanics, particle in a box, harmonic oscillator, rigid rotor, hydrogen atom, approximate methods, multielectron atoms, chemical bonding, NMR, and particle in a ring.