Vibration–rotation interaction in the rigid bender: A quantum mechanical phase space view

In this paper, we examine classical–quantum correspondence in a system with strong vibration–rotation interaction. We study the quantum mechanics of a two degree of freedom rigid bender Hamiltonian, previously considered in the context of classical mechanics by Ezra [Chem. Phys. Lett. 127, 492 (1986)] and by Frederick and McClelland [J. Chem. Phys. 84, 4347 (1986)]. Eigenfunctions and eigenvalues of this system are calculated by matrix diagonalization in a harmonic oscillator–rigid rotor basis. The quantum mechanics are compared with the classical mechanics by visualizing the quantum eigenstates on a surface of section, defined in terms of the coherent states of the rotor and oscillator. We find clear connections between eigenstate structure on the quantum surface of section and features of the classical phase space, such as nonlinear resonance, period doubling, and chaos.