Physics – Quantum Physics
Scientific paper
2003-12-10
Physics
Quantum Physics
6 pages, 4 figures
Scientific paper
10.1088/0305-4470/37/24/L03
Notwithstanding radical conceptual differences between classical and quantum mechanics, it is usually assumed that physical measurements concern observables common to both theories . Not so with the eigenvalues ($\pm 1$) of the parity operator. The effect of such a measurement on a mixture of even and odd states of the harmonic oscillator is akin to separating at a single stroke a pair of shuffled card decks: the result is a set of definite parity, though otherwise mixed. The Wigner function should be a sensitive probe for this phenomenon, for it can be interpreted as the expectation value of the parity operator. We here derive the general form of Wigner functions $W_{\pm}$, resulting from an ideal parity measurement on $W(\x)$. Even if $W(\x)$ resembles a classical distribution, $W_{\pm}$ displays a quantum spike, which is positive for $W_+$ and negative for $W_-$. However we conjecture that $W_+$ always has negative values.
Brodier Olivier
de Almeida Alfredo M. Ozorio
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