我們將研究下列問題: 1. 在本計劃中, 我們將繼續探討鮑利及狄拉克方程在不同的電磁 場下的準精確可解性。我們希望能把過去的工作推廣到以更高階的李 代數為基礎的準精確可解模型, 及相關的QES 準正規模系統。我們也 準備探討多粒子系統的準精確可解模型。 2. 我們將繼續探討量子系統在週期外場重的穩定性問題。我們將 考慮其他能以解析法, 近似法, 或數值法處理的位壘, 以及不同的場振 盪模式。 3. 我們將更深入的探討奇性位勢中可包容束敷態的奇特例子。 4. 我們將進一步研究一類由我們導出的離散FokkerPlanck 方程 的性質。 We shall continue to investigate the following problems: 1. the quasi-exact solvability of the Pauli and Dirac equations with various external field configurations. We hope to extend our previous works to quasi-exactly solvable models based on higher Lie- algebras. We will examine one-dimensional multi-particle quasi-exactly solvable physical systems ; 2. we will also continue our investigations of the stability problem of a quantum system in time-dependent fields which could be treated either analytically, approximately, or numerically; 3. we shall study more deeply the strange cases of bound states in singular potentials; 4. we shall also study the properties of the new class of discrete Fokker-Planck equations derived by us recently.
