τ-Schrödinger Equation

The τ-Schrödinger equation is the τ-categorical statement of unitary time evolution on the holomorphic state space of the τ-framework. It emerges as a structural theorem from the categorical kernel and the holomorphic-state-space construction — not as a postulate.

Categorical invariant. i ℏ_τ ∂_t ψ = Ĥ ψ on the τ-holomorphic state space; ψ is a section of a τ-categorical bundle and Ĥ is the τ-energy operator.

Primary registry anchor: IV.T28

Supporting items: IV.D14, IV.D11

1. I.K0 — Universe Postulate
2. IV.D11 — Physical Quantity Template
3. IV.D14 — Uncertainty Product establishes Heisenberg-style duality at the categorical level
4. IV.T28 — Schrödinger Equation derived as a τ-categorical theorem

Calibration anchor: PG-P01-neutron

Calibration chain:

1. ℏ_τ from ι_τ-chain
2. energy-time duality at τ-natural unit scale
3. SI bridge via m_n anchor for energy units

Manuscript reference: manuscript-sources/book-04/part02/ch16-holomorphic-quantization.tex

Status: Planned

Related glossary entries

• PG-Q01-mass Mass
• PG-U01-tau-second τ-Second

Referenced by

• PG-L02-tau-heisenberg-uncertainty τ-Heisenberg Uncertainty
• PG-L03-tau-maxwell-system τ-Maxwell System (Complete)
• PG-L04-tau-einstein-equation τ-Einstein Equation
• PG-L07-tau-navier-stokes-regularity τ-Navier–Stokes Regularity
• PG-L08-tau-noether-theorem τ-Noether Theorem
• PG-O01-hydrogen-atom Hydrogen Atom
• PG-O05-helium-atom Helium Atom
• PG-O06-electron-orbital Electron Orbital