 Particle number from Bogoliubov coefficients

ID: particle-number-from-bogoliubov-coefficients

Codex  0 Created 2026-09-28 Updated 2026-10-06

u_{i}^{out} = \sum_{j} (α_{ij} u_{j}^{in} + β_{ij} u_{j}^{in *}),

then the expected out-particle number in mode

i

in the in-vacuum is

⟨ 0_{in} ∣ N_{i}^{out} ∣ 0_{in} ⟩ = \sum_{j} ∣ β_{ij} ∣^{2} .

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