Umbral calculus, discretization, and quantum mechanics on a lattice

被引：24

作者：

Dimakis, A ^{[1
]}

MullerHoissen, F ^{[1
]}

Striker, T ^{[1
]}

机构：

[1] INST THEORET PHYS, D-37073 GOTTINGEN, GERMANY

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 1996年 / 29卷 / 21期

关键词：

D O I：

10.1088/0305-4470/29/21/017

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

'Umbral calculus' deals with representations of the canonical commutation relations. We present a short exposition of it and discuss how this calculus can be used to discretize continuum models and to construct representations of Lie algebras on a lattice. Related ideas appeared in recent publications and we show that the examples treated there are special cases of umbral calculus. This observation then suggests various generalizations of these examples. A special umbral representation of the canonical commutation relations given in terms of the position and momentum operator on a lattice is investigated in detail.

引用

页码：6861 / 6876

页数：16

共 28 条

[1] LORENTZ TRANSFORMATION ON THE LATTICE [J].