Quantum Mechanics in Theoretical Physics
( 25 Modules )

Module #1
Introduction to Quantum Mechanics
Overview of quantum mechanics, historical background, and key concepts

Module #2
Wave-Particle Duality
Wave-like and particle-like behavior of quantum systems, experimentally verified

Module #3
Mathematical Preliminaries
Review of linear algebra, vector calculus, and differential equations

Module #4
Schrödinger Equation
Time-dependent and time-independent forms, solutions, and physical interpretation

Module #5
Wave Functions and Probability
Wave function as a mathematical representation, probability amplitudes and densities

Module #6
Operators and Measurements
Linear operators, Hermitian operators, and measurement outcomes

Module #7
Spectral Theory
Eigenvalues, eigenvectors, and the spectral decomposition theorem

Module #8
Position and Momentum
Position and momentum operators, commutation relations, and the uncertainty principle

Module #9
Energy and Time-Evolution
Energy eigenvalues, time-evolution operators, and the Schrödinger picture

Module #10
Particle in a Box
Bound states, energy quantization, and wave functions for a particle in a box

Module #11
Harmonic Oscillator
Quantization of energy, ladder operators, and coherent states

Module #12
Angular Momentum
Angular momentum operators, eigenvalues, and spin

Module #13
Central Potential
Radial wave functions, spherical harmonics, and bound states

Module #14
Identical Particles
Wave functions for identical particles, symmetrization, and anti-symmetrization

Module #15
Scattering Theory
Scattering matrix, S-matrix, and cross-sections

Module #16
Interference and Entanglement
Quantum interference, entanglement, and EPR paradox

Module #17
Quantum Systems with Internal Degrees of Freedom
Spin, isospin, and other internal degrees of freedom

Module #18
Many-Body Systems
Many-particle systems, Hartree-Fock approximation, and density functional theory

Module #19
Quantum Field Theory
Introduction to QFT, quantization of fields, and particle creation/annihilation operators

Module #20
Relativistic Quantum Mechanics
Klein-Gordon equation, Dirac equation, and relativistic wave functions

Module #21
Quantum Mechanics in Electromagnetic Fields
Landau levels, Zeeman effect, and quantum Hall effect

Module #22
Quantum Information and Computation
Qubits, quantum gates, and quantum algorithms

Module #23
Quantum Measurement and Decoherence
Measurement theory, wave function collapse, and decoherence

Module #24
Applications of Quantum Mechanics
Chemical bonding, molecular spectra, and condensed matter physics

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

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