Exact Polynomial Solutions of Schrdinger Equation with Various Hyperbolic Potentials |
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作者姓名: | 温发楷 杨战营 刘冲 杨文力 张耀中 |
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基金项目: | Supported by the National Natural Science Foundation of China under Grant Nos.11047025,11075126 and 11031005;the Ministry of Education Doctoral Program Funds under Grant Nos.20126101110004,20116101110017;SRF for ROCS |
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摘 要: | The Schrdinger equation with hyperbolic potential 2V(x) =-V0sinhq(x/d)/cosh6(x/d)(q = 0, 1, 2, 3) is studied by transforming it into the confluent Heun equation. We obtain general symmetric and antisymmetric polynomial solutions of the Schrdinger equation in a unified form via the Functional Bethe ansatz method. Furthermore, we discuss the characteristic of wavefunction of bound state with varying potential strengths. Particularly, the number of wavefunction's nodes decreases with the increase of potential strengths, and the particle tends to the bottom of the potential well correspondingly.
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关 键 词: | Schrdinger equation hyperbolic potential the functional Bethe ansatz method exact polynomial solutions |
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