### 用高斯展开法数值求解薛定谔方程的Mathematica实现及算法分析 评分:

Mathematica 51 Lvectors--Transpose vectors ] DiagonalMatrix[values 上 Igenvectors LH“H. Transpose vectors」=N. Transpose vectors. DiagonalMatrix values」”. Mathematica 5. o Cornell 40 10 N=40 N=10 13.6055 112.319 l0.4573 10.4574 3.40136 13.566 1.94049 1.94C72 1.51171 C.434638 0.467697 0.850298 1.44928 13.4755 0.544123 0.802061 l158.2 0.531781 9836 29836 O.275291 0.386866 680605 680604 0.200442 0.279977 1.51694×107 1.51686×107 0.00770283 0.00785407 3.36474×10 35814×10 71=0.015;rN=17000 3.2 100 Cornell Potential: V(r) 4 Cornell Potential: V(r-p H 3.1 -13.6eV N=10 r a cholesky 2.8 Choicsk -15 71 o auto 2.7 :=0015au m=1.35 GeV 画200 r=1/137 2.6 0.20G~V2 -250 5000100001500020000 20000400006000080000100000 1 Cornell IS Chloesky) 1/ Cornell GEM (3-4) 1994-2012cHinaAcademicJournalElectronicPublishingHouse.Allrightsreservedhttp://www.cnki.net 52 http://xbbjhswucn 0.75 AuTO H Cholesky 0,50 06 Charmonium in cornell potential 0.25 04 0.00 00 -0.50 =0015a.u r=0.4 -0.75 rx1000 N2.2 tm 1.00 Y Auto Mathematica E Eigenvalues QR El genvalues Math ematica Cholesky [1] KEN P F, GROSSE H, SCH F. Solving the Schrodinger Equation for Bound States [J]. Comp Phys Commun, 1985 21 KOONIN S E, MEREDITH D C. Computational Physics[M|. New York: Addison-Wesley. 1990 [3 KAMIMURA M. Nonadiabatic Coupled-Rcarrangcment Channel Approach to Mounic Molcculcs [J]. Phys Rev A 1988,38:621-624. [4 HIYAMA E, KAMIMURA M, MOTOBA T, et al. Three-Body Model Study of A=6-7 Hypernuclei: Halo and Skin Structures [J. Phys Rev C,1996, 53: 2075-2085 51 HIYAMA E, KAMIMURA M, MOTOBA T, et al. Three and Four-Body Cluster Models of Hypernuclei Using the G MEtrix AN Intcraction- Bc,C, A Hc and 4-[J. Prog Theor Phys, 1997,97: 881-899. L6 HIYAMA E, KAMIMURA M, Miyazaki K, et al. y Transitions in A-7 Hypernuclei and a Possible Derivation cf Hy- pernuclear Size [j]. Phys Rev C,1999, 59: 2351-2360 L7 HIYAMA E, KAMIMURA M. MOTOBA T, et al. AN Spin-Orbit Splittings in A Be and A C Studisd witn One-Boson- Exchang AN Interactions J. Phys Rev Lett, 2000,85: 270-273 L8 HIYAMA E, KAMIMURA M, MOTOBA T, et al. A-2 Conversion in A He and H Based on a Four-Body Calculation 1994-2012cHinaAcademicJournalElectronicPublishingHouse.Allrightsreservedhttp://www.cnki.net Mathematica 53 LJ]. Phys Rev c,2001,65:011301-011305 [9 HIYAMA E, KAMIMURA M, MOTOBA T,et al. Four-Body Cluster Structure of A==7-10 Double-A Hypernuclei J. Phys Rev(,2002,66:024007-204019 [10 HIYAMA E, KINO Y, KAMIMURA M. Gaussian Expansion Method for Few-Body Systems [J]. Progress in Particle and Nuclear Physics, 2C03, 51: 223-307 L11」 MATLAB 2007:346-351. 12] Mathematica ,2010:217 13] ,1980. 14] ,1986:384-530 [15] EICHTEN E, GOTTFRID K, KINOSHITA T. Charmonium: Camparison with Experiment [J_. Phys Rev D, 1980 21:203-233. Mathematica Programming and Algorithm Analysis of Solving Schrodinger Equation with Gaussian Expansion Method CAo Lu, chen hong School of Physical Science and Technology, Southwest University, Chongging 400715, China Abstract: Gaussians expansion method has been regarded as an efficient and non-perturbative technique for the calculations of energy eigenvalue problems. In this paper, the divergence of correlations between basis spaces and the two different available algorithms is analyzed in case of two-body bounding state. The choice of gaussian basis is discussed for hydrogen atom and charmonium bounded by cornell potential as examples, and the standard energy spectra and the corresponding wave functions are obtained Key words: Gaussians expanding method Schrodinger equation; generalized eigenvalues 1994-2012cHinaAcademicJournalElectronicPublishingHouse.Allrightsreservedhttp://www.cnki.net

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