Abstract:
A study is made of the problem of diagonal operators on a two-dimensional sphere. A trigonometrie
form of an elliptic system of coordinates on a sphere that is convenient for applications
in physics is derived. Wave eigenfunctions of diagonal operators in the elliptic coordinate
system – so-called spheroconieal functions – are constructed. Their main properties
are derived. Conditions that determine the eigenvalues of the second diagonal operator
in the elliptic coordinate system are found. Some matrix elements of spheroconicM functions
are calculated. Possible applications in physics are discussed for the complete set of
quantum-mechanical observables associated with the elliptic coordinate system on the twodimensional
sphere.
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