Canonical transformations and accidental degeneracy. II. The isotropic oscillator in a sector

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Abstract
In this paper we discuss the accidental degeneracy in the problem of a particle in two dimensional oscillator potential constrained to move in a sector of angle π/q,q integer. The degeneracy is due to both the Hamiltonian and the boundary conditions. The symmetry Lie group of canonical transformations is suggested by the explicit form of a complete nonorthonormal set of states expressed in terms of the creation operators. This group is complex and the corresponding representation in quantum mechanics is nonunitary. We discuss briefly the appearance of complex canonical transformations in physical problems.