Periodic Toda lattice in quantum mechanics

Journal Article · Tue Dec 01 04:00:00 EST 1992 · Annals of Physics (New York); (United States)

DOI:https://doi.org/10.1016/0003-4916(92)90365-S· OSTI ID:6821751

Matsuyama, A ^[1]

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1. Shizuoka Univ. (Japan)

The quantum mechanical periodic Toda lattice is studied by the direct diagonalization of the Hamiltonian. The eigenstates are classified according to the irreducible representations of the dihedral group D[sub N]. It is shown that Gutzwiller's quantization conditions are satisfied and they have a one-to-one correspondence to the irreducible representation of the D[sub N] group. The authors have also carried out the semiclassical quantization of the periodic Toda lattice by the EBK formulation. The eigenvalues of the semiclassical quantization have a one-to-one correspondence to the integer quantum numbers, and those quantum numbers also have a close relationship to the symmetry of the state. Numerical calculations have been done for N = 3, 4, 5, and 6 particle periodic Toda lattices. The distributions of the eigenvalues are systematic and distinguished by the symmetry of the state. As illustrative examples, amplitudes of the wave functions and density distributions are shown. 14 refs., 8 figs., 11 tabs.

• OSTI ID: 6821751
• Journal Information: Annals of Physics (New York); (United States), Journal Name: Annals of Physics (New York); (United States) Vol. 220:2; ISSN APNYA6; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

661100* -- Classical & Quantum Mechanics-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EIGENSTATES
EIGENVALUES
ENERGY-LEVEL DENSITY
FUNCTIONS
HAMILTONIANS
IRREDUCIBLE REPRESENTATIONS
MASS
MATHEMATICAL OPERATORS
MECHANICS
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
ONE-DIMENSIONAL CALCULATIONS
QUANTUM MECHANICS
QUANTUM NUMBERS
QUANTUM OPERATORS
VARIATIONS
WAVE FUNCTIONS