Atomic and Molecular Physics
Coulomb Potential Energy
Two-Body Problem Reduction
Center-of-Mass Transformation
Reduced Mass
Separation of Variables in Spherical Coordinates
Radial Equation
Angular Equation
The Radial Schrödinger Equation
Effective Potential
Centrifugal Barrier Term
Asymptotic Behavior
Series Solution Method
Associated Laguerre Polynomials
Normalization of Radial Functions
Principal Quantum Number n
Physical Meaning and Allowed Values
Orbital Angular Momentum Quantum Number l
Magnetic Quantum Number m_l
Energy Level Formula
Degeneracy of Energy Levels
Accidental Degeneracy in Hydrogen
Complete Wavefunctions
Radial Wavefunctions
Radial Nodes
Radial Probability Distribution
Angular Wavefunctions
Spherical Harmonics
Atomic Orbitals
s Orbitals (l = 0)
p Orbitals (l = 1)
d Orbitals (l = 2)
f Orbitals (l = 3)
Orbital Shapes and Orientations
Probability Density Plots
Nodal Surfaces
Radial and Angular Nodes
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2. Simple Quantum Systems
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4. Fine Structure and Relativistic Effects