{
    "api": "YAML JSON TOON Database",
    "version": "1.0.0",
    "format": "json",
    "dataset": {
        "id": 477,
        "slug": "quantum-mechanics-basics",
        "title": "Quantum Mechanics: Core Principles and Phenomena",
        "description": "Foundations of quantum mechanics: wave-particle duality, Schr\u00f6dinger equation, Heisenberg uncertainty, quantum superposition, entanglement, and measurement problem.",
        "category": "Physics",
        "category_slug": "physics",
        "tags": "physics,quantum-mechanics,schrodinger,heisenberg,superposition,entanglement,wave-particle-duality",
        "view_count": 3,
        "created_at": 1781275786,
        "updated_at": 1781275786
    },
    "data": {
        "principles": [
            {
                "name": "Wave-Particle Duality",
                "description": "Matter and light exhibit both wave and particle properties depending on experimental setup",
                "key_experiments": [
                    "Double-slit experiment (interference pattern for electrons\/photons)",
                    "Photoelectric effect (light as particles\/photons)",
                    "Davisson-Germer experiment (electron diffraction)"
                ],
                "formula": "de Broglie wavelength: \u03bb = h\/p",
                "significance": "Fundamental departure from classical physics; all matter has wave nature"
            },
            {
                "name": "Schr\u00f6dinger Equation",
                "description": "Fundamental equation of non-relativistic quantum mechanics; describes evolution of quantum state",
                "formula": "i\u210f \u2202\u03c8\/\u2202t = \u0124\u03c8 (time-dependent); \u0124\u03c8 = E\u03c8 (time-independent)",
                "significance": "Predicts probability amplitudes; solutions (wavefunctions) give energy levels and spatial distributions",
                "interpretation": "|\u03c8(x)|\u00b2 gives probability density of finding particle at position x"
            },
            {
                "name": "Heisenberg Uncertainty Principle",
                "description": "Fundamental limit on simultaneous precision of complementary observables",
                "formula": "\u0394x \u00b7 \u0394p \u2265 \u210f\/2; \u0394E \u00b7 \u0394t \u2265 \u210f\/2",
                "significance": "Not a measurement limitation but intrinsic property of quantum systems; conjugate variables cannot be simultaneously sharp",
                "implications": "Explains atomic stability (electron can't collapse into nucleus), zero-point energy"
            },
            {
                "name": "Quantum Superposition",
                "description": "Quantum system exists in all possible states simultaneously until measured",
                "formula": "|\u03c8\u27e9 = \u03b1|0\u27e9 + \u03b2|1\u27e9 where |\u03b1|\u00b2 + |\u03b2|\u00b2 = 1",
                "significance": "Basis of quantum computing (qubits); demonstrated by double-slit interference",
                "famous_example": "Schr\u00f6dinger's cat thought experiment (cat simultaneously alive and dead)"
            },
            {
                "name": "Quantum Entanglement",
                "description": "Two or more particles share a quantum state; measurement of one instantaneously affects the other regardless of distance",
                "formula": "|\u03c8\u27e9 = (|00\u27e9 + |11\u27e9)\/\u221a2 (Bell state)",
                "significance": "Violates local realism (Bell's theorem); basis for quantum cryptography and teleportation",
                "experimental_verification": "Aspect experiment (1982) confirmed Bell inequality violation; 2022 Nobel Prize"
            },
            {
                "name": "Quantum Measurement (Collapse)",
                "description": "Measurement causes wavefunction to collapse to an eigenstate of the measured observable",
                "interpretations": [
                    {
                        "name": "Copenhagen",
                        "description": "Collapse is fundamental; measurement creates reality"
                    },
                    {
                        "name": "Many-Worlds",
                        "description": "No collapse; all outcomes realized in branching universes"
                    },
                    {
                        "name": "Decoherence",
                        "description": "Apparent collapse due to entanglement with environment"
                    }
                ],
                "significance": "Measurement problem remains unresolved; central mystery of quantum foundations"
            },
            {
                "name": "Pauli Exclusion Principle",
                "description": "No two identical fermions can occupy the same quantum state simultaneously",
                "formula": "\u03c8(r\u2081,r\u2082) = -\u03c8(r\u2082,r\u2081) (antisymmetric wavefunction for fermions)",
                "significance": "Explains electron shell structure, periodic table, stability of matter, neutron star degeneracy pressure",
                "applies_to": "Fermions (electrons, protons, neutrons, quarks); not bosons (photons, gluons)"
            }
        ]
    }
}