https://doi.org/10.1007/s100530050164
Quantum theory of rotation angles: The problem of angle sum and angle difference
Departamento de Óptica, Facultad de Ciencias Físicas,
Universidad Complutense, 28040 Madrid, Spain
Corresponding author: a lsanchez@eucmax.sim.ucm.es
Received:
6
December
1997
Revised:
15
April
1998
Accepted:
7
May
1998
Published online: 15 August 1998
We reconsider the problem of the sum and
difference of two angle variables in quantum mechanics.
The spectra of the sum and difference operators have
widths of 
, but angles differing by 
are
indistinguishable. This means that the angle sum and
difference probability distributions must be cast into
a range. We obtain probability distributions
for the angle sum and difference and relate this
problem to the representation of nonbijective
canonical transformations.
PACS: 03.65.Bz – Foundations, theory of measurement, miscellaneous theories (including Aharonov Bohm effect, Bell inequalities, Berry's phase) / 42.50.Dv – Nonclassical field states; squeezed, antibunched, and sub-Poissonian states; operational definitions of the phase of the field; phase measurements
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1998
