theorem
proved
term proof
schrodinger_i_from_8tick
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formal statement (Lean)
134theorem schrodinger_i_from_8tick :
135 -- The i in Schrödinger equation is the 8-tick generator
136 -- It ensures unitary (phase-preserving) evolution
137 ∀ (ψ : ℝ → ℂ) (H : ℂ → ℂ) (ℏ : ℝ),
138 (∀ t, ψ t = cexp (I * (-H (ψ t) * t / ℏ))) →
139 ∃ (phase_gen : ℂ), phase_gen = I ∧ phase_gen = eightTickPhase 2 := by
proof body
Term-mode proof.
140 intro ψ H ℏ h_evol
141 use I
142 constructor
143 · rfl
144 · exact tick2_is_i.symm
145
146/-! ## Euler's Formula -/
147
148/-- Euler's formula: e^{iθ} = cos(θ) + i·sin(θ)
149
150 This is the bridge between:
151 - Exponential functions (growth/decay)
152 - Trigonometric functions (oscillation)
153 - Complex numbers (rotation)
154
155 All unified by the 8-tick phase structure! -/