In this approach, the quantum many-body states are represented in the Fock state basis, which are constructed by filling up each single-particle state with a certain number of identical particles.
42.
Where " i " ranges over all possible molecular conditions . ( ! denotes factorial . ) The " correction " in the denominator is because identical particles in the same condition are indistinguishable.
43.
This theorem has an interpretation in terms of particle-paths : when identical particles are present, the integral over all intermediate particles must not double-count states that differ only by interchanging identical particles.
44.
This theorem has an interpretation in terms of particle-paths : when identical particles are present, the integral over all intermediate particles must not double-count states that differ only by interchanging identical particles.
45.
:Identical particles have the same rest mass, electric charge, and spin angular momentum, but can be distinguished by position, linear momentum, orbital angular momentum, and direction of the spin angular momentum.
46.
As described in the article on identical particles, this implies that the state of the entire system must be either symmetric ( bosons ) or antisymmetric ( fermions ) when the coordinates of its constituent particles are exchanged.
47.
Besides these practical applications of BEC in interferometry, the quantum statistical approach [ 10 ] has led to quite an unexpected heuristic application, related to the principle of identical particles, the fundamental starting point of BEC.
48.
:68.40.57.1-- This question actually is very significant in quantum theory, where there's a difference between " bosons " and " fermions "; see article Identical particles.
49.
For non-interacting identical particles, the potential is still a sum, but wavefunction is a bit more complicated it is a sum over the permutations of products of the separate wavefunctions to account for particle exchange.
50.
For a collection of particles, some identical with coordinates and others distinguishable ( not identical with each other, and not identical to the aforementioned identical particles ), the wave function is symmetric or antisymmetric in the identical particle coordinates only:
