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ABSTRACT. In this announcement we describe the asymptotic behavior of the spectrum of the quantum mechanical spherical pendulum as Planck's constant tends to zero.We begin by discussing 1. The classical spherical pendulum [6, 4]. As a Hamiltonian system the spherical pendulum has a configuration spaceand a phase spaceThe standard symplectic form X)f=i ^Q% A dpi on R 3 x R

We s h ow t hat t he h ydrogen atom in orthogonal electric and m agnetic elds has a special property of certain integrable classical Hamiltonian systems known as monodromy. T h e strength o f t he elds is assumed to b e s m all enough to v alidate t he u s e o f a normal form H snf which i s o b t ained from a two s t ep normalization of the o r i g i n al system. We c o n s i d er the l e v el sets o f H snf on the second r e d uced phase space. For an open set of eld parameters we s h ow t hat t here is a special dynamically invariant s e t which is a \doubly pinched 2-torus". This implies that t he i n tegrable Hamiltonian H snf has monodromy. Manifestation of monodromy in quantum m echanics is also discussed.