The quantum phase problem: steps toward a resolution

Details The quantum phase problem: steps toward a resolution The quantum phase problem: steps toward a resolution

2001-07-24

arxiv.org/abs/quant-ph/0107122v2

Found.Phys. 32 (2002) 907-926

Physics

Quantum Physics

21 pages, REVTEX

Scientific paper

Defining the observable ${\bf \phi}$ canonically conjugate to the number observable ${\bf N}$ has long been an open problem in quantum theory. The problem stems from the fact that ${\bf N}$ is bounded from below. In a previous work we have shown how to define the absolute phase observable ${\bf \Phi}\equiv |{\bf\phi}|$ by suitably restricting the Hilbert space of $x$ and $p$ like variables. Here we show that also from the classical point of view, there is no rigorous definition for the phase even though it's absolute value is well defined.

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