Spectral Analysis of Certain Schrodinger Operators
Spectral Analysis of Certain Schrodinger Operators
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DOI：
10.3842/sigma.2012.061
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发表时间：
2012-05
影响因子：
0.9
通讯作者：
M. Ismail;E. Koelink
中科院分区：
文献类型：
--
作者：
M. Ismail;E. Koelink
The J-matrix method is extended to difference and q-difference operators and is applied to several explicit differential, difference, q-difference and second order Askey{ Wilson type operators. The spectrum and the spectral measures are discussed in each case and the corresponding eigenfunction expansion is written down explicitly in most cases. In some cases we encounter new orthogonal polynomials with explicit three term recurrence relations where nothing is known about their explicit representations or orthogonality mea- sures. Each model we analyze is a discrete quantum mechanical model in the sense of Odake and Sasaki (J. Phys. A: Math. Theor. 44 (2011), 353001, 47 pages).
