| Quantum Mechanics A
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Schrödinger Equation
The most fundamental equation of quantum mechanics; given a Hamiltonian Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathcal{H}}
, it describes how a state Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle |\Psi\rangle}
evolves in time.
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Basic Concepts and Theory of Motion
UV Catastrophe (Black-Body Radiation)
Photoelectric Effect
Stability of Matter
Double Slit Experiment
Stern-Gerlach Experiment
The Principle of Complementarity
The Correspondence Principle
The Philosophy of Quantum Theory
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Brief Derivation of Schrödinger Equation
Relation Between the Wave Function and Probability Density
Stationary States
Heisenberg Uncertainty Principle
Some Consequences of the Uncertainty Principle
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Linear Vector Spaces and Operators
Commutation Relations and Simultaneous Eigenvalues
The Schrödinger Equation in Dirac Notation
Transformations of Operators and Symmetry
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One-Dimensional Bound States
Oscillation Theorem
The Dirac Delta Function Potential
Scattering States, Transmission and Reflection
Motion in a Periodic Potential
Summary of One-Dimensional Systems
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Harmonic Oscillator Spectrum and Eigenstates
Analytical Method for Solving the Simple Harmonic Oscillator
Coherent States
Charged Particles in an Electromagnetic Field
WKB Approximation
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The Heisenberg Picture: Equations of Motion for Operators
The Interaction Picture
Time Evolution of Expectation Values and Ehrenfest's Theorem
The Virial Theorem
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Feynman Path Integrals
The Free-Particle Propagator
Harmonic Oscillator: Saddle-Point Action
Harmonic Oscillator: Integration Over Fluctuations
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Commutation relations
Angular momentum as a generator of rotations in 3D
Spherical Coordinates
Eigenvalue quantization
Orbital angular momentum eigenfunctions
Problems on Angular Momentum
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Generalized derivation
Free particle in spherical coordinates
Spherical well
Isotropic Harmonic Oscillator
Hydrogen atom
WKB in spherical coordinates
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Differential cross-section and the Green's function formulation of scattering
Central potential scattering and phase shifts
Born approximation and examples of cross-section calculations
Coulomb potential scattering
Two particle scattering
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