Abstract
Let us consider a superposition | ψ> obtained from ψ0> by action of some operation T̂(τj), where τj is complex and N is a normalization constant. The probability distribution for some observable Ậ which commutes with T̂ (τj), having eigenstates | n> corresponding to the eigenvalues an is where we assume that the eigenvalues of T̂n(τj) are Tn(τj) = exp (i λn θj), for real λn and θj. For a superposition of N states obtained by regularly transforming | ψ0>, such that θj+1 – θj = 2φ, one has where in the interference term of classical diffraction. Besides the interference term, a diffraction term appears, proportional to the square of the overlap between the state | ψ0> and the eigenstate | n>, and is analogous to the form factor of classical diffraction. The maxima of the function S(N, λn φ) occur for λn φ = υ π (υ = 0, ±1 ±2, …), thus the distribution Pn has an oscillatory character. We have thus the diffraction grating in phase space.
© 1992 IQEC
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