theorem
proved
term proof
born_normalization
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formal statement (Lean)
100theorem born_normalization (theta : ℝ) :
101 Real.sin theta ^ 2 + Real.cos theta ^ 2 = 1 :=
proof body
Term-mode proof.
102 Real.sin_sq_add_cos_sq theta
103
104/-! ## Mesoscopic Threshold -/
105
106/-- The mesoscopic threshold: the mass at which A ≈ 1 (the transition
107 between quantum coherence and classical behavior).
108
109 m_coh ≈ 0.2 ng = 2e-13 kg for τ ≈ 1 s.
110
111 Below m_coh: quantum superpositions survive (A << 1)
112 Above m_coh: rapid decoherence (A >> 1) -/