{"query": "The quantum harmonic oscillator — zero-point and the ladder", "count": 20, "results": [{"id": "card_chart_quantum_harmonic_oscillator", "title": "The quantum harmonic oscillator — zero-point and the ladder", "shelf": "codex", "surface": "secular", "snippet": "A chart on the one map: the tick stick stick_the_quantum_harmonic_oscillator_zero_point_and_the_ladder, placed on the quantum-mechanics floor. The oscillator's ground state is 1/2 hbar omega (the zero", "authority_tier": "engine_derived", "source": "Narrow Highway - a chart: a tick stick placed on the one map", "readable": false, "generated": false}, {"id": "card_n_cdb747a427d2", "title": "Electronics — the resonant chain, from Ohm's law to the radio wave", "shelf": "science", "surface": "secular", "snippet": "One sealed chain runs the whole bench: Ohm's law (V = I·R), the capacitor's\nexponential clock (one time constant → 63.2% charged), the diode's exponential gate (current\ndoubles every ln2·nVT ≈ 17.9 mV", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}, {"id": "card_bridge_theory_elasticity__acoustic_wave_theory", "title": "Bridge: Elasticity (Hooke's law, stress–strain)  ↔  Acoustic wave theory (harmonics, Doppler)", "shelf": "bridges", "surface": "secular", "snippet": "Elasticity (Hooke's law, stress–strain) and Acoustic wave theory (harmonics, Doppler) are the same form in different domains. Hooke's linear restoring force gives the harmonic oscillator, and a contin", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_calc_molecular_vibration", "title": "Molecular bond vibration", "shelf": "calculations", "surface": "secular", "snippet": "Molecular bond vibration — chemistry. Formula: omega = sqrt(k/mu). Canonical FORM: periodic (x = A*cos(omega*t + phi)) — a chemical bond is a spring — the harmonic oscillator with the reduced mass mu ", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_n_c39a51a03b6f", "title": "Oscillator — LC resonance, the bench's own Schumann", "shelf": "science", "surface": "secular", "snippet": "Energy sloshing between a coil and a capacitor rings at f = 1/(2π√(LC)); sealed:\n100 µH with 100 pF gives 1.591 MHz — the middle of the AM broadcast band: https://narrowhighway.com/s/1ee0d3ed486453eee", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}, {"id": "card_calc_quantum_oscillator", "title": "Quantum harmonic oscillator", "shelf": "calculations", "surface": "secular", "snippet": "Quantum harmonic oscillator — physics. Formula: E_n = hbar omega (n + 1/2). Canonical FORM: periodic (x = A*cos(omega*t + phi)) — the oscillator quantized — evenly-spaced energy levels above a zero-po", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_sys_wave", "title": "Waves & oscillation", "shelf": "systems", "surface": "secular", "snippet": "The same wave equation governs sound in air, light in the field, ripples on water, and a plucked string. The same harmonic oscillator is an LC circuit, a mass on a spring, and a pendulum — resonance a", "authority_tier": "reference", "source": "The recurring form — the system analogies (standard engineering) + the design they witness to", "readable": false, "generated": false}, {"id": "card_calc_lattice_vibration", "title": "Lattice phonons", "shelf": "calculations", "surface": "secular", "snippet": "Lattice phonons — condensed_matter. Formula: omega(k) = 2 sqrt(K/m) |sin(ka/2)|. Canonical FORM: periodic (x = A*cos(omega*t + phi)) — a crystal's vibrations are a chain of coupled harmonic oscillator", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_src_openstax_university_physics_volume_3_7_5_the_quantum_harmonic_oscillator_c0e31b3b", "title": "7.5 The Quantum Harmonic Oscillator — University Physics Volume 3", "shelf": "physics", "surface": "secular", "snippet": "7.5\n\nThe Quantum Harmonic Oscillator\n\nLearning Objectives\nBy the end of this section, you will be able to:\n\nDescribe the model of the quantum harmonic oscillator\n\nIdentify differences between the clas", "authority_tier": "reference", "source": "OpenStax: University Physics Volume 3 (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_n_9d42516b140c", "title": "Quartz at 32,768 Hz — a power of two on the wrist", "shelf": "science", "surface": "secular", "snippet": "Every quartz watch cuts a tuning fork to hum at exactly 2^15 = 32,768 Hz, sealed, and\n32768 / 2^15 = 1: run the signal through fifteen binary flip-flops, each halving the frequency,\nand the last ticks", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}, {"id": "card_c_106861f9474c", "title": "Varactor — tuning by voltage ↔ Oscillator — LC resonance, the bench's own S", "shelf": "connections", "surface": null, "snippet": "since f ∝ 1/√C, halving the capacitance raises the frequency by exactly √2  — a concord the card itself states; mined + verified.", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "readable": false, "generated": false}, {"id": "card_bridge_master_harmonic_oscillator", "title": "Master equation: d2x/dt2 = -omega^2 x", "shelf": "bridges", "surface": "secular", "snippet": "a restoring force proportional to displacement — every oscillation is this, with omega^2 = restoring/inertia. ONE equation, 4 domains, connected by a change of variable: physics [omega^2 = k/m (spring", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_c_f746297fd660", "title": "Schumann resonance — the Earth-ionosphere ca ↔ Oscillator — LC resonance, the bench's own S", "shelf": "connections", "surface": null, "snippet": "the cavity is an oscillator, lightning the impulse source, a Schumann receiver just a coil and an amplifier  — a concord the card itself states; mined + verified.", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "readable": false, "generated": false}, {"id": "card_src_openstax_university_physics_volume_3_introduction_018ccaf5", "title": "Introduction — University Physics Volume 3", "shelf": "physics", "surface": "secular", "snippet": "Figure\n7.1\n\nA D-wave qubit processor: The brain of a quantum computer that encodes information in quantum bits to perform complex calculations. (credit: modification of work by D-Wave Systems, Inc.)\n\n", "authority_tier": "reference", "source": "OpenStax: University Physics Volume 3 (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_c_b94b0e3c6dfb", "title": "Radio-wave production — the chain leaves the ↔ Oscillator — LC resonance, the bench's own S", "shelf": "connections", "surface": null, "snippet": "Drive an antenna with the oscillator and the wave departs at c: λ = c/f — sealed:\nthe 1.591 MHz LC wave is ≈ 188 m long (floor(c·2π·10⁻⁷) = 188)  — a concord the card itself states; mined + verified.", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "readable": false, "generated": false}, {"id": "card_c_45b1fde0f875", "title": "Quartz at 32,768 Hz — a power of two on the  ↔ Oscillator — LC resonance, the bench's own S", "shelf": "connections", "surface": null, "snippet": "It is the highest power of two that stays low-power and stable — the oscillator meeting the divider chain.  — a concord the card itself states; mined + verified.", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "readable": false, "generated": false}, {"id": "card_src_openstax_college_physics_ap_courses_16_5_energy_and_the_simple_harmonic_osci_111ed811", "title": "16.5 Energy and the Simple Harmonic Oscillator — College Physics for AP® Courses", "shelf": "physics", "surface": "secular", "snippet": "16.5\n\nEnergy and the Simple Harmonic Oscillator\n\nLearning Objectives\n\nBy the end of this section, you will be able to:\n\nDescribe the changes in energy that occur while a system undergoes simple harmon", "authority_tier": "reference", "source": "OpenStax: College Physics for AP® Courses (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_openstax_college_physics_16_5_energy_and_the_simple_harmonic_osci_85b8cd63", "title": "16.5 Energy and the Simple Harmonic Oscillator — College Physics", "shelf": "physics", "surface": "secular", "snippet": "16.5\n\nEnergy and the Simple Harmonic Oscillator\n\nTo study the energy of a simple harmonic oscillator, we first consider all the forms of energy it can have We know from Hooke’s Law: Stress and Strain ", "authority_tier": "reference", "source": "OpenStax: College Physics (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_openstax_college_physics_2e_16_5_energy_and_the_simple_harmonic_osci_85b8cd63", "title": "16.5 Energy and the Simple Harmonic Oscillator — College Physics 2e", "shelf": "physics", "surface": "secular", "snippet": "16.5\n\nEnergy and the Simple Harmonic Oscillator\n\nLearning Objectives\n\nBy the end of this section, you will be able to:\n\nDetermine the maximum speed of an oscillating system.\n\nTo study the energy of a ", "authority_tier": "reference", "source": "OpenStax: College Physics 2e (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_openstax_college_physics_ap_courses_2e_16_5_energy_and_the_simple_harmonic_osci_85b8cd63", "title": "16.5 Energy and the Simple Harmonic Oscillator — College Physics for AP® Courses 2e", "shelf": "physics", "surface": "secular", "snippet": "16.5\n\nEnergy and the Simple Harmonic Oscillator\n\nLearning Objectives\n\nBy the end of this section, you will be able to:\n\nDetermine the maximum speed of an oscillating system.\n\nTo study the energy of a ", "authority_tier": "reference", "source": "OpenStax: College Physics for AP® Courses 2e (CC-BY 4.0)", "readable": false, "generated": false}], "house": {"door": "FIND", "kind": "cards", "trail": "results", "seal": null, "next_step": {"do": "open the top card", "door": "FIND", "tool": "card_get", "params": {"id": "card_chart_quantum_harmonic_oscillator"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}