Exponential Lattices as Regularizers in Quantum Mechanics

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概要

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• By discretizing Schrodinger operators within the framework of bilateral Jacobi matrices, acting in l^2, one obtains a regularization procedure for Rayleigh-Schrodinger perturbation series.The mathematical background of this procedure is elaborated and fits into Kato's theory of regular perturbations.Considering a discretized oscillator algebra, one can relate these general results to concrete examples of anharmonic oscillators.The obtained results clearly support the basic strategies of lattice field theories with high complexity : Compared to quantum mechanics, it is well known that there exist more sophisticated, but in principle similar procedures in lattice quantum chromodynamics.Also the exponential lattice that we will consider imposes a regularization of singularities.By this q-lattice regularization, these singularities drop out of the Rayleigh-Schrodinger series we address.

• 理論物理学刊行会の論文
• 2000-07-14

著者

• Ruffing L.

  Center Of Mathematical Sciences

• Ruffing Andreas

  Center Of Mathematical Sciences

関連論文

• Exponential Lattices as Regularizers in Quantum Mechanics
• Lattice Phonon Operators and Selfsimilar Superpotentials

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