Quantum mechanical Liouville model with attractive potential

Jan, 1996
20 pages
Published in:
  • Nucl.Phys.B 472 (1996) 409-426
e-Print:
Report number:
  • INS-1124

Citations per year

19962003201020172024102
Abstract:
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 θ[0,2π)\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.
Note:
  • 20 pages, plain tex, 2 Postscript figures Report-no: INS-Rep.-1124
  • 03.65.Db
  • Hamiltonian reduction
  • Liouville potential
  • Self-adjoint extension
  • field theory: Liouville
  • quantization
  • Hamiltonian formalism
  • quantum mechanics
  • potential
  • numerical calculations