Department of Mathematics2024-11-0920100375-960110.1016/j.physleta.2010.10.0502-s2.0-78449280089http://dx.doi.org/10.1016/j.physleta.2010.10.050https://hdl.handle.net/20.500.14288/9544We offer a new Hamiltonian formulation of the classical Pais-Uhlenbeck oscillator and consider its canonical quantization. We show that for the non-degenerate case where the frequencies differ, the quantum Hamiltonian operator is a Hermitian operator with a positive spectrum, i.e., the quantum system is both stable and unitary. Furthermore it yields the classical Pais-Uhlenbeck oscillator in the classical limit. A consistent description of the degenerate case based on a Hamiltonian that is quadratic in momenta requires its analytic continuation into a complex Hamiltonian system possessing a generalized PT-symmetry (an involutive antilinear symmetry). We devise a real description of this complex system, derive an integral of motion for it, and explore its quantization.PhysicsJournal Article1873-2429285127000006Q25484