State orthogonality, boson bunching parameter and bosonic enhancement factor

Abstract: It is emphasized that the bunching parameter β ≡p_B/p_D,i.e. the ratio between the probability to measure two bosons and two distinguishableparticles at the same state, is a constant of motion and depends only on the overlapbetween the initial wavefunctions. This ratio is equal to β = 2 / (1 +I²), where I is the overlap integralbetween the initial wavefunctions. That is, only when the initial wavefunctions areorthogonal this ratio is equal to 2, however, this bunching ratio can be reduced to 1,when the two wavefunctions are identical. This simple equation explains the experimentalevidences of a beam splitter. A straightforward conclusion is that by measuring thelocal bunching parameter β (at any point in space and time) it is possibleto evaluate a global parameter I (the overlap between the initial wavefunctions).The bunching parameter is then generalized to arbitrary number of particles, and in ananalogy to the two-particles scenario, the well-known bosonic enhancement appears onlywhen all states are orthogonal. Graphical abstract: [Figure not available: see fulltext.]