MPEJ Volume 4, No.2, 19pp
Received: Dec 17, 1997, Revised: Mar 18, 1998, Accepted: May 14, 1998
N. Ripamonti
Classical Limit of the Matrix Elements on Quantized Lobachevskii Plane
ABSTRACT: It is proved that the matrix elements $\wh F_{n,n+k}$ between
harmonic oscillator eigenvectors of any smooth observable in the quantized
Lobachevskii plane converge to the Fourier coefficients $F_{k}$ of the
corresponding classical observable $F(A,\phi)$ at the classical limit
$n\to\infty, \hbar\to 0, n\hbar\to A$, $k$ fixed, where $A$, $\phi$ are
the oscillator action-angle variables. The Wigner functions are then
defined and, as a consequence of the above result, their convergence to
$\delta(A-A_{0})e^{-ik\phi}$ at the classical limit is proved when
computed on the harmonic oscillator eigenstates $n$ and $n+k$.