Quantum 101

Table of Contents Introduction What Are Probability Amplitudes? Mathematical Definition Born Rule and Measurement Superposition Principle Inner Products and Transition Amplitudes Amplitudes in Different Representations Probability Densities and Continuum States Normalization and Orthogonality Interference...

Table of Contents Introduction The Schrödinger Equation Framework Time-Dependent vs Time-Independent Equations Derivation from Separation of Variables Mathematical Form of the Time-Independent Schrödinger Equation Physical Interpretation Boundary Conditions and Normalization One-Dimensional Potential...

Table of Contents Introduction Quantum States and Hilbert Space Bra-Ket Notation Properties of State Vectors Orthogonality and Completeness Observables as Operators Hermitian Operators and Measurement Eigenvalues and Eigenvectors Expectation Values and Variance Operator Algebra Commutators...

Table of Contents Introduction Why Postulates? Postulate 1: State Vector and Hilbert Space Postulate 2: Observables and Operators Postulate 3: Measurement and Expectation Values Postulate 4: Time Evolution and Schrödinger...

Table of Contents Introduction Historical Context and the Failure of Classical Models Basic Postulates of Bohr’s Model Quantization of Angular Momentum Energy Levels of the Hydrogen Atom Spectral Lines and...

Table of Contents Introduction Historical Background Classical Wave Behavior Young’s Original Experiment Single-Photon and Single-Electron Double-Slit Experiments Interference Patterns and Quantum Superposition Quantum Mechanical Description Probability Amplitudes and the Born Rule Which-Path Information...

Table of Contents Introduction Historical Background What Is Compton Scattering? Classical Wave Prediction Compton’s Experiment Derivation of the Compton Shift Key Equations and Interpretation Conservation of Energy and Momentum The Compton Wavelength Experimental Validation Implications...

Table of Contents Introduction Historical Context Light as a Wave Light as a Particle The Double-Slit Experiment de Broglie’s Hypothesis Matter Waves and Electron Diffraction Wave-Particle Duality of Photons Wave-Particle Duality of Electrons Interference...

Table of Contents Introduction What Is the Photoelectric Effect? Classical Prediction and Its Failure Experimental Observations Einstein’s Quantum Hypothesis Mathematical Description Threshold Frequency and Work Function Kinetic Energy of Emitted Electrons Role of...

Table of Contents Introduction What Is a Blackbody? Classical Approach and the Ultraviolet Catastrophe Rayleigh–Jeans Law and Its Limitations Wien’s Empirical Law Planck’s Quantum Hypothesis Derivation of Planck’s Law Energy Quantization and...

Table of Contents Introduction The Classical Crisis: Failure of Classical Physics Blackbody Radiation and Planck’s Hypothesis The Photoelectric Effect and Einstein’s Light Quanta Atomic Spectra and Bohr’s Model Compton Scattering...

Table of Contents Introduction Why Python and Julia for Physics? Core Language Features for Scientific Computing Numerical Computing in Python Symbolic and Analytical Computation in Python Visualization with Python Julia's Philosophy...