Foundations of Quantum Mechanics
( 25 Modules )

Module #1
Introduction to Quantum Mechanics
Overview of classical mechanics, wave-particle duality, and the need for quantum mechanics

Module #2
Wave Functions and Wave Equations
Definition of wave functions, wave equations, and their physical interpretation

Module #3
Mathematical Preliminaries
Review of linear algebra, vector spaces, and Hilbert spaces

Module #4
Schrödinger Equation
Time-dependent and time-independent Schrödinger equations, and their solutions

Module #5
Wave Packet Dynamics
Free particle wave packets, group velocity, and wave packet spreading

Module #6
Bound States and Potential Wells
Infinite and finite potential wells, energy quantization, and wave functions

Module #7
Tunneling and Barrier Penetration
Classical-quantum analogy, tunneling probability, and applications

Module #8
Angular Momentum and Spin
Classical and quantum angular momentum, spin, and spin-statistics theorem

Module #9
Stern-Gerlach Experiment and Spin Measurement
Historical significance, experimental setup, and quantum mechanical analysis

Module #10
Entanglement and Bells Theorem
Definition of entanglement, EPR paradox, Bells inequality, and implications

Module #11
Quantum Measurement and the Copenhagen Interpretation
Measurement problem, wave function collapse, and the Copenhagen interpretation

Module #12
Heisenberg Uncertainty Principle
Mathematical formulation, physical implications, and uncertainty relations

Module #13
Quantization of Harmonic Oscillators
Classical harmonic oscillators, quantization, and energy eigenvalues

Module #14
Ladder Operators and Algebraic Methods
Creation and annihilation operators, algebraic methods, and applications

Module #15
Hydrogen Atom and Central Potentials
Schrödinger equation for hydrogen atom, energy levels, and wave functions

Module #16
Scattering Theory and Cross-Sections
Time-dependent and time-independent scattering, Born approximation, and cross-sections

Module #17
Many-Electron Atoms and Spin-Statistics Theorem
Hartree-Fock method, exchange energy, and spin-statistics connection

Module #18
Quantum Systems in External Fields
Zeeman effect, Stark effect, and quantum systems in electromagnetic fields

Module #19
Density Matrices and Quantum Ensembles
Definition of density matrices, pure and mixed states, and quantum ensembles

Module #20
Entropy and Information Theory
Von Neumann entropy, Shannon entropy, and connections to information theory

Module #21
Quantum Computing and Quantum Information
Introductions to quantum computing, qubits, and quantum algorithms

Module #22
Interference and Coherence
Double-slit experiment, coherence, and interference in quantum systems

Module #23
Decoherence and the Environment
Decoherence mechanisms, environmental effects, and the loss of quantum coherence

Module #24
Quantum Foundations and Interpretations
Overview of different interpretations, such as Copenhagen, Many-Worlds, and pilot-wave theory

Module #25
Course Wrap-Up & Conclusion
Planning next steps in Foundations of Quantum Mechanics career

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