  The concept of mutually unbiased bases is studied for N pairs of continuous
variables. To find mutually unbiased bases reduces, for specific states related
to the Heisenberg-Weyl group, to a problem of symplectic geometry. Given a
single pair of continuous variables, three mutually unbiased bases are
identified while five such bases are exhibited for two pairs of continuous
variables. For N = 2, the golden ratio occurs in the definition of these
mutually unbiased bases suggesting the relevance of number theory not only in
the finite-dimensional setting.
