Quantum mechanical Liouville model with attractive potential
Jan, 199620 pages
Published in:
- Nucl.Phys.B 472 (1996) 409-426
e-Print:
- hep-th/9601111 [hep-th]
Report number:
- INS-1124
View in:
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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 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
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