{"query": "Madelung hydrodynamics — quantum mechanics as a probability", "count": 20, "results": [{"id": "card_n_810d857d886e", "title": "Madelung hydrodynamics — quantum mechanics as a probability fluid", "shelf": "science", "surface": "secular", "snippet": "Write ψ = √ρ·e^(iS/ħ) and the Schrödinger equation becomes fluid dynamics of the probability\ndensity ρ = |ψ|²: a continuity equation with velocity v = ∇S/m, plus an Euler equation carrying a\n'quantum "}, {"id": "card_c_41cd8b933961", "title": "Fluid probability dynamics — one continuity  ↔ Madelung hydrodynamics — quantum mechanics a", "shelf": "connections", "surface": null, "snippet": "quantum mechanics (Madelung: v = ∇S/m plus a quantum potential — the Schrödinger equation rewritten as fluid dynamics of |ψ|²)  — a concord the card itself states; mined + verified."}, {"id": "card_c_576d28632055", "title": "Madelung hydrodynamics instantiates Fluid probability dynamics", "shelf": "connections", "surface": null, "snippet": "Quantum mechanics rewritten as the fluid dynamics of |ψ|²."}, {"id": "card_n_8530c72a2201", "title": "Fluid probability dynamics — one continuity equation across physics, geometry, and ML", "shelf": "science", "surface": "secular", "snippet": "One equation wears many clothes. Probability is a conserved fluid: the continuity equation\ndρ/dt + ∇·J = 0 (current J = ρv) says density is never created or destroyed — it only flows. The\nsame skeleto"}, {"id": "card_src_word_quantum_mechanics", "title": "quantum mechanics", "shelf": "dictionary", "surface": "secular", "snippet": "quantum mechanics: (noun) the branch of quantum physics that accounts for matter at the atomic level; an extension of statistical mechanics based on quantum theory (especially the Pauli exclusion prin"}, {"id": "card_src_word_wave_mechanics", "title": "wave mechanics", "shelf": "dictionary", "surface": "secular", "snippet": "wave mechanics: (noun) the modern form of quantum theory; an extension of quantum mechanics based on Schrodinger's equation; atomic events are explained as interactions between particle waves"}, {"id": "card_src_word_quantum_jump", "title": "quantum jump", "shelf": "dictionary", "surface": "secular", "snippet": "quantum jump: (noun) (physics) an abrupt transition of an electron or atom or molecule from one quantum state to another with the emission or absorption of a quantum · (noun) a sudden large increase o"}, {"id": "card_c_b0dd29a6dbce", "title": "The periodic table — the map of the elements ↔ Madelung hydrodynamics — quantum mechanics a", "shelf": "connections", "surface": null, "snippet": "its periodicity is the fingerprint of the quantum shells beneath  — a concord the card itself states; mined + verified."}, {"id": "card_src_word_classical_mechanics", "title": "classical mechanics", "shelf": "dictionary", "surface": "secular", "snippet": "classical mechanics: (noun) the branch of mechanics based on Newton's laws of motion — syn: Newtonian mechanics"}, {"id": "card_src_word_newtonian_mechanics", "title": "newtonian mechanics", "shelf": "dictionary", "surface": "secular", "snippet": "newtonian mechanics: (noun) the branch of mechanics based on Newton's laws of motion — syn: classical mechanics"}, {"id": "card_src_word_quantum", "title": "quantum", "shelf": "dictionary", "surface": "secular", "snippet": "quantum: (noun) a discrete amount of something that is analogous to the quantities in quantum theory · (noun) (physics) the smallest discrete quantity of some physical property that a system can posse"}, {"id": "card_src_word_conditional_probability", "title": "conditional probability", "shelf": "dictionary", "surface": "secular", "snippet": "conditional probability: (noun) the probability that an event will occur given that one or more other events have occurred — syn: contingent probability"}, {"id": "card_src_word_contingent_probability", "title": "contingent probability", "shelf": "dictionary", "surface": "secular", "snippet": "contingent probability: (noun) the probability that an event will occur given that one or more other events have occurred — syn: conditional probability"}, {"id": "card_src_book_66078", "title": "A Treatise on Mechanics — Henry Kater", "shelf": "gutenberg", "surface": "secular", "snippet": "A Treatise on Mechanics, by Henry Kater. Subjects: Mechanics. Read the full text (public domain): https://www.gutenberg.org/ebooks/66078"}, {"id": "card_src_book_33663", "title": "The Origin and Development of the Quantum Theory — Max Planck", "shelf": "gutenberg", "surface": "secular", "snippet": "The Origin and Development of the Quantum Theory, by Max Planck. Subjects: Quantum theory. Read the full text (public domain): https://www.gutenberg.org/ebooks/33663"}, {"id": "card_src_book_47167", "title": "On the Quantum Theory of Line-Spectra, Part 1 and 2 — Niels Bohr", "shelf": "gutenberg", "surface": "secular", "snippet": "On the Quantum Theory of Line-Spectra, Part 1 and 2, by Niels Bohr. Subjects: Quantum theory; Spectrum analysis. Read the full text (public domain): https://www.gutenberg.org/ebooks/47167"}, {"id": "card_src_book_72800", "title": "The quantum postulate and the recent development of atomic theory — Niels Bohr", "shelf": "gutenberg", "surface": "secular", "snippet": "The quantum postulate and the recent development of atomic theory, by Niels Bohr. Subjects: Quantum theory; Atoms. Read the full text (public domain): https://www.gutenberg.org/ebooks/72800"}, {"id": "card_src_book_73087", "title": "On the quantum theory of radiation and the structure of the atom — Niels Bohr", "shelf": "gutenberg", "surface": "secular", "snippet": "On the quantum theory of radiation and the structure of the atom, by Niels Bohr. Subjects: Quantum theory; Atomic structure. Read the full text (public domain): https://www.gutenberg.org/ebooks/73087"}, {"id": "card_src_book_49445", "title": "Mechanics: The Science of Machinery — A. Russell (Alexander Russell) Bond", "shelf": "gutenberg", "surface": "secular", "snippet": "Mechanics: The Science of Machinery, by A. Russell (Alexander Russell) Bond. Subjects: Machinery; Mechanics; Mechanical engineering. Read the full text (public domain): https://www.gutenberg.org/ebook"}, {"id": "card_src_word_quantum_leap", "title": "quantum leap", "shelf": "dictionary", "surface": "secular", "snippet": "quantum leap: (noun) a sudden large increase or advance — syn: quantum jump"}]}