Threshold conditions and bound states for locally periodic delta potentials

Marappan Dharani, B. Sahu, C. Shastry
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引用次数: 5

Abstract

We present a systematic study of the conditions for the generation of threshold energy eigen states and also the energy spectrum generated by two types of locally periodic delta potentials each having the same strength λV and separation distance parameter a: (a) sum of N attractive potentials and (b) sum of pairs of attractive and repulsive potentials. Using the dimensionless parameter g = λV a in case (a) the values of g = gn, n = 1, 2, …, N at which threshold energy bound state gets generated are shown to be the roots of Nth order polynomial D1(N, g) in g. We present an algebraic recursive procedure to evaluate the polynomial D1(N, g) for any given N. This method obviates the need for the tedious mathematical analysis described in our earlier work to generate D1(N, g). A similar study is presented for case (b). Using the properties of D1(N, g) we establish that in case (a) the critical minimum value of g which guarantees the generation of the maximum possible number of bound states is g = 4. The corresponding result for case (b) is g = 2. A typical set of numerical results showing the pattern of variation of gn as a function of n and several interesting features of the energy spectrum for different values of g and N are also described.
局部周期δ势的阈值条件和束缚态
我们系统地研究了产生阈值能量本征态的条件,以及由两种具有相同强度λV和分离距离参数a的局部周期δ势所产生的能谱:(a) N个吸引势和(b)一对吸引和排斥势和。使用无量纲参数g =λV以防(a)的值g = gn, n = 1, 2,…,n的阈值能量束缚态显示生成的根源n阶多项式D1 (n, g)在g。我们提出一个代数递归过程评估多项式D1 (n, g)对于任何给定的n .这个方法可以不再需要我们的早期作品中描述的乏味的数学分析生成D1 (n, g)。类似的研究提出了为例(b)。使用D1的属性(n,G)我们建立了在情形(a)下保证产生最大可能约束态数的G的临界最小值为G = 4。情形(b)的对应结果为g = 2。还描述了一组典型的数值结果,显示了gn作为n的函数的变化模式,以及不同g和n值时能谱的几个有趣特征。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Central European Journal of Physics
Central European Journal of Physics 物理-物理:综合
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审稿时长
3.3 months
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