We calculate the variance characterizing the distribution of transitio
n amplitudes for the hydrogen atom in a strong magnetic field, where t
he transition amplitudes are available experimentally. For two operato
rs, namely ($) over cap Z and ($) over cap P-2, we find excellent agre
ement between the quantum variances and the corresponding semi-classic
al approximations. We show that the semi-classical analysis is conside
rably simplified by making use of the scaling property of the system.