Quantum mechanical Liouville model with attractive potential

Details Quantum mechanical Liouville model with attractive potential Quantum mechanical Liouville model with attractive potential

1996-01-22

arxiv.org/abs/hep-th/9601111v1

Nucl.Phys. B472 (1996) 409-426

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, plain tex, 2 Postscript figures

Scientific paper

10.1016/0550-3213(96)00230-1

We study the quantum mechanical Liouville model with attractive potential which is obtained by Hamiltonian symmetry reduction from the system of a free particle on $SL(2, \Real)$. The classical reduced system consists of a pair of Liouville subsystems which are `glued together' in such a way that the singularity of the Hamiltonian flow is regularized. It is shown that the quantum theory of this reduced system is labelled by an angle parameter $\theta \in [\,0,2\pi)$ characterizing the self-adjoint extensions of the Hamiltonian and hence the energy spectrum. There exists a probability flow between the two Liouville subsystems, demonstrating that the two subsystems are also `connected' quantum mechanically, even though all the wave functions in the Hilbert space vanish at the junction.

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