{"id": "card_chart_quantum_harmonic_oscillator", "kind": "reference", "title": "The quantum harmonic oscillator — zero-point and the ladder", "body": "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-point, forced by uncertainty), its levels an evenly-spaced ladder E_n = (n + 1/2) hbar omega. Every potential near its minimum is a QHO, and every quantum field is a set of oscillators whose rungs are particles - the bridge to the Standard Model. The stick keeps its seals (read live at /stick?id=stick_the_quantum_harmonic_oscillator_zero_point_and_the_ladder); this card is a cited pointer, not a copy. Found, never generated.", "source": {"label": "Narrow Highway - a chart: a tick stick placed on the one map", "url": "", "ref": "stick_the_quantum_harmonic_oscillator_zero_point_and_the_ladder", "authority_tier": "engine_derived"}, "shelf": "codex", "box": "chart", "bands": ["chart", "stick", "quantum harmonic oscillator", "zero-point", "one map"], "subject": "The quantum harmonic oscillator - zero-point and the ladder", "connections": [{"to_card_id": "card_floor_quantum_mechanics", "relationship": "charts", "evidence": "the zero-point and the ladder - the oscillator forced by uncertainty, on the quantum floor"}, {"to_card_id": "card_floor_standard_model", "relationship": "connects_at", "evidence": "the field-as-oscillators bridge: a particle is a quantum of a field's harmonic oscillator"}, {"to_card_id": "card_k_floor_of_discovery", "relationship": "part_of", "evidence": "a chart on the one map, rooted in the Floor of Discovery"}], "author": "engine", "created_at": 0.0, "updated_at": 0.0, "visibility": "public", "lifecycle_stage": "public", "volatility": "permanent", "surface": "secular", "generated": false, "call": "codex.chart", "facets": {"subject": ["one map", "quantum harmonic oscillator", "stick", "zero-point"]}, "presentation": {"glyph": "•", "kind_label": "chart", "by": "Narrow Highway - a chart: a tick stick placed on the one map", "authority": "engine_derived", "posted": "", "standing": ""}, "neighbors": [{"id": "card_floor_quantum_mechanics", "title": "Quantum mechanics — the quantum and its limits", "relationship": "charts", "why": "the zero-point and the ladder - the oscillator forced by uncertainty, on the quantum floor", "href": "/card/card_floor_quantum_mechanics", "resolved": true}, {"id": "card_floor_standard_model", "title": "The floor of the Standard Model - where two trees meet", "relationship": "connects at", "why": "the field-as-oscillators bridge: a particle is a quantum of a field's harmonic oscillator", "href": "/card/card_floor_standard_model", "resolved": true}, {"id": "card_k_floor_of_discovery", "title": "The Floor of Discovery — one floor, and by its design the fear of God", "relationship": "part of", "why": "a chart on the one map, rooted in the Floor of Discovery", "href": "/card/card_k_floor_of_discovery", "resolved": true}], "house": {"door": "FIND", "kind": "card", "trail": "connections", "seal": "/card/card_chart_quantum_harmonic_oscillator", "next_step": {"do": "follow a connection: what this card rests on, and what rests on it", "door": "FIND", "tool": "card_connections", "params": {"id": "card_chart_quantum_harmonic_oscillator"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}