Eigenvalue comparisons for quantum systems in a box |
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| Affiliation: | 1. Key Laboratory of Natural Medicine and Immune-Engineering of Henan Province, Henan University, Kaifeng, Henan, 475004, PR China;2. College of Public Health, Zhengzhou University, Zhengzhou, 450001, PR China;1. Department of Lifelong Learning and Extension, Institute of Rural Reconstruction, Palli Samgathana Vibhaga, Visva-Bharati, Santiniketan, 731235, India;2. Department of Environmental Studies, Institute of Science, Siksha Bhavan, Visva-Bharati, Santiniketan, 731235, India |
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| Abstract: | Comparison theorems are obtained for the first even and odd solutions of Schrödinger's equation −v″ + Q(t)v = λv, −l ≤ t ≤ l with boundary conditions v(−l) = v(l) = 0. The comparison functions Qi(t), i = 1, 2, may intersect at a finite number of points within [−l,l]. Immediate extensions are possible for a more general class of Sturm-Liouville problems, and for problems in unbounded regions. |
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