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178
Sub Topics
263
MCQs
116
MCOs
186
True/False
116
Fill Blanks
35
Rearrange
103
Matching
57
Comprehensions
103
Flashcard Decks
Curriculum
What You'll Learn
01 Foundations of Quantum Mechanics 3 topics
1 Historical Development
- Blackbody Radiation and Planck's Quantum Hypothesis
- Photoelectric Effect and Einstein's Photon Theory
- Bohr's Atomic Model
- De Broglie's Matter Waves
- Compton Effect
- Heisenberg's Uncertainty Principle
2 Experimental Foundations
- Double-Slit Experiment
- Stern-Gerlach Experiment
- Davisson-Germer Experiment
3 Mathematical Preliminaries
- Linear Vector Spaces
- Hermitian Operators
- Dirac Notation
- Eigenvalue Problems
02 Quantum Mechanical Formalism 5 topics
1 Wave Functions and Probability Interpretation
- Normalization
- Expectation Values
- Probability Density
2 Schrödinger Equation
- Time-Dependent Form
- Time-Independent Form
- Stationary States
3 Operators and Observables
- Position and Momentum Operators
- Commutation Relations
- Compatible and Incompatible Observables
4 Heisenberg's Matrix Mechanics
- Matrix Representation
- Equivalence to Wave Mechanics
5 Dirac's Formulation
- Ket and Bra Vectors
- Transformation Theory
03 One-Dimensional Quantum Systems 4 topics
1 Free Particle
- Plane Wave Solutions
- Wave Packets
- Group and Phase Velocity
2 Potential Wells
- Infinite Square Well
- Finite Square Well
- Quantum Tunneling
3 Quantum Harmonic Oscillator
- Algebraic Solution
- Hermite Polynomials
- Energy Eigenvalues and Eigenfunctions
- Coherent States
4 Scattering in One Dimension
- Transmission and Reflection Coefficients
- Step Potential
- Barrier Penetration
- Resonant Tunneling
04 Angular Momentum 4 topics
1 Orbital Angular Momentum
- Operators and Eigenvalues
- Spherical Harmonics
- Selection Rules
2 Spin Angular Momentum
- Stern-Gerlach Experiment Revisited
- Pauli Matrices
- Spin-1/2 Systems
3 Addition of Angular Momenta
- Clebsch-Gordan Coefficients
- Total Angular Momentum
- Spectroscopic Notation
4 Magnetic Effects
- Zeeman Effect
- Spin-Orbit Coupling
05 Three-Dimensional Systems 4 topics
1 Central Potentials
- Separation of Variables
- Radial Equation
- Effective Potential
2 Hydrogen Atom
- Schrödinger Solution
- Quantum Numbers
- Hydrogen Wavefunctions
3 Identical Particles
- Symmetrization Principle
- Bosons and Fermions
- Pauli Exclusion Principle
- Exchange Energy
4 Multi-Electron Atoms
- Electron Configuration
- Hund's Rules
- Periodic Table Structure
06 Approximation Methods 4 topics
1 Time-Independent Perturbation Theory
- Non-Degenerate Case
- Degenerate Case
- Applications to Atomic Physics
2 Variational Method
- Rayleigh-Ritz Procedure
- Trial Functions
- Applications
3 WKB Approximation
- Semiclassical Approach
- Connection Formulas
- Tunneling in WKB
4 Time-Dependent Perturbation Theory
- Fermi's Golden Rule
- Harmonic Perturbations
- Transition Rates
07 Quantum Dynamics 4 topics
1 Time Evolution
- Schrödinger Picture
- Heisenberg Picture
- Interaction Picture
2 Density Matrix Formalism
- Pure and Mixed States
- Reduced Density Matrix
- Partial Trace
3 Quantum Oscillations
- Two-Level Systems
- Rabi Oscillations
- Quantum Beats
4 Sudden and Adiabatic Approximations
- Adiabatic Theorem
- Geometric Phase (Berry Phase)
08 Scattering Theory 4 topics
1 Partial Wave Analysis
- Phase Shifts
- Cross Sections
- Optical Theorem
2 Born Approximation
- First and Second Order Terms
- Validity Conditions
3 Resonance Scattering
- Breit-Wigner Formula
- Feshbach Resonances
4 Inelastic Scattering
- Form Factors
- Inelastic Cross Sections
09 Relativistic Quantum Mechanics 4 topics
1 Klein-Gordon Equation
- Free Particle Solutions
- Probability Current
- Negative Energy States
2 Dirac Equation
- Dirac Matrices
- Relativistic Covariance
- Electron Spin
- Antimatter
3 Quantum Electrodynamics: Introduction
- Quantization of the Electromagnetic Field
- Photons
- Vacuum Fluctuations
4 Relativistic Effects in Atoms
- Fine Structure Revisited
- Lamb Shift
- Hyperfine Structure
10 Symmetries and Conservation Laws 5 topics
1 Symmetry Transformations
- Continuous and Discrete Symmetries
- Unitary Operators
2 Conservation Laws
- Noether's Theorem
- Energy, Momentum, Angular Momentum
3 Parity
- Space Inversion
- Parity of Wavefunctions
- Selection Rules
4 Time Reversal
- Kramers Degeneracy
- Anti-Unitary Operators
5 Gauge Symmetry
- U(1) Gauge Transformation
- Physical Significance
11 Quantum Entanglement and Measurement 4 topics
1 Composite Systems
- Tensor Product Spaces
- Entangled States
- Schmidt Decomposition
2 Quantum Measurement
- Projective Measurements
- POVM Measurements
- Collapse Postulate
3 EPR Paradox and Bell's Inequalities
- EPR Argument
- Hidden Variables
- Bell's Theorem
- Experimental Tests
4 Quantum Decoherence
- Environment-Induced Decoherence
- Quantum to Classical Transition
- Decoherence Time Scales
12 Applications of Quantum Mechanics 4 topics
1 Atomic Physics
- Multi-Electron Spectra
- Selection Rules
- Lasers and Masers
2 Molecular Physics
- Born-Oppenheimer Approximation
- Molecular Bonds
- Vibrational and Rotational Spectra
3 Solid State Physics
- Crystal Structures
- Band Theory
- Conductors, Insulators, and Semiconductors
- Quantum Wells and Superlattices
4 Nuclear Physics
- Nuclear Models
- Radioactive Decay
- Nuclear Reactions
13 Quantum Information and Computing 4 topics
1 Quantum Bits (Qubits)
- Bloch Sphere Representation
- Multiple Qubits
2 Quantum Gates and Circuits
- Universal Gate Sets
- Circuit Diagrams
3 Quantum Algorithms
- Deutsch-Jozsa Algorithm
- Grover's Search Algorithm
- Shor's Factoring Algorithm
4 Quantum Error Correction
- Quantum Error Models
- Stabilizer Codes
- Fault Tolerance
14 Interpretations of Quantum Mechanics 5 topics
1 Copenhagen Interpretation
- Bohr's Complementarity
- Wave Function Collapse
2 Many-Worlds Interpretation
- Universal Wavefunction
- Branching Universes
3 Hidden Variables Theories
- Bohmian Mechanics
- Contextuality
4 Consistent Histories
- Decoherent Histories
- Logical Framework
5 Quantum Bayesianism
- QBism
- Subjective Probability
15 Advanced Topics in Quantum Theory 4 topics
1 Path Integral Formulation
- Feynman Path Integrals
- Propagators
- Stationary Phase Approximation
2 Quantum Field Theory: Fundamentals
- Second Quantization
- Creation and Annihilation Operators
- Fock Space
3 Quantum Many-Body Systems
- Quantum Statistical Mechanics
- Phase Transitions
- Superconductivity and Superfluidity
4 Topological Quantum Phenomena
- Quantum Hall Effect
- Topological Insulators
- Anyons and Fractional Statistics
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Quantum Mechanics
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