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Exact solutions of the Schrodinger equation with inverse-power potential
Dong SH(董世海); Ma ZQ(马中骐); Dong, SH; Ma, ZQ; Esposito, G
1999
发表期刊FOUNDATIONS OF PHYSICS LETTERS
卷号12期号:5页码:465-474
通讯作者Inst High Energy Phys, Beijing 100039, Peoples R China ; China Ctr Adv Sci & Technol, World Lab, Beijing 100080, Peoples R China ; Ist Nazl Fis Nucl, Sez Napoli, I-80125 Naples, Italy ; Complesso Univ Monte S Angelo, Dipartimento Sci Fis, I-80126 Naples, Italy
文章类型Article
摘要The Sckrodinger equation for stationary states is studied in a central potential V(r) proportional to r(-beta) in an arbitrary number of spatial dimensions. The presence of a single term in the potential makes it impossible to use previous algorithms, which only work for quasi-exactly-solvable problems. Nevertheless, the analysis of the stationary Schrodinger equation in the neighbourhood of the origin and of the point at infinity is found to provide relevant information about the desired solutions for all values of the radial coordinate. The original eigenvalue equation is mapped into a differential equation with milder singularities, and the role played by the particular case beta = 4 is elucidated. In general, whenever the parameter beta is even and larger than 4, a recursive algorithm for the evaluation of eigenfunctions is obtained. Eventually, in the particular case of two spatial dimensions, the exact form of the ground-state wave function is obtained for a potential containing a finite number of inverse powers of r, with the associated energy eigenvalue.
关键词quantum mechanics scattering states bound states
学科领域Physics
研究领域[WOS]Physics ; Physics
DOI10.1023/A:1021633411616
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语种英语
研究领域[WOS]Physics ; Physics
WOS类目Physics, Multidisciplinary
WOS记录号WOS:000084204700005
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被引频次:55[WOS]   [WOS记录]     [WOS相关记录]
文献类型期刊论文
条目标识符http://ir.ihep.ac.cn/handle/311005/237595
专题理论物理室
作者单位中国科学院高能物理研究所
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GB/T 7714
Dong SH,Ma ZQ,Dong, SH,et al. Exact solutions of the Schrodinger equation with inverse-power potential[J]. FOUNDATIONS OF PHYSICS LETTERS,1999,12(5):465-474.
APA 董世海,马中骐,Dong, SH,Ma, ZQ,&Esposito, G.(1999).Exact solutions of the Schrodinger equation with inverse-power potential.FOUNDATIONS OF PHYSICS LETTERS,12(5),465-474.
MLA 董世海,et al."Exact solutions of the Schrodinger equation with inverse-power potential".FOUNDATIONS OF PHYSICS LETTERS 12.5(1999):465-474.
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