On energy gaps in a new type of analytically solvable model in quantum mechanics
On energy gaps in a new type of analytically solvable model in quantum mechanics
复制标题
关于量子力学中新型解析可解模型中的能隙
DOI：
10.1016/0022-247x(88)90003-0
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发表时间：
1988
影响因子：
1.3
通讯作者：
W. Kirsch
中科院分区：
文献类型：
--
作者：
F. Gesztesy;H. Holden;W. Kirsch
分析了由− d2 <$dx2 +∑ j∈ Z β j δ′（x− yj），β j，yj ∈ R给出的一类新的解析可解的一维量子力学模型.除了计算这种δ′-（和δ-）模型的各种周期排列的态密度外，我们还证明了Saxon-Hutner猜想的推广，该猜想涉及δ-或δ′-相互作用的某些“替代合金”的能谱中存在能隙。此外，还研究了相应的随机Hamiltonian（即{β j} j∈ Z遍历随机过程）的谱，并在某些情况下明确地确定了谱.
A new type of analytically solvable, one-dimensional model in quantum mechanics formally given by− d 2⧸ dx 2+∑ j∈ Z β j δ′(x− y j), β j, y j∈ R is analyzed. Besides calculating the density of states of various periodic arrangements of such δ′-(and δ-) models we also prove a generalization of the Saxon-Hutner conjecture concerning the existence of gaps in the energy spectrum of certain “substitutional alloys” of δ-or δ′-interactions. In addition the spectrum of the corresponding random Hamiltonians (ie,{β j} j∈ Z ergodic stochastic processes) is investigated and explicitly determined in certain cases.