Chinese Physics C > 2003, Vol. 27 > Issue(3): 215-222

Green Function Iterative Solution of Ground State Wave Function for Yukawa Potential

ZHANG Zhao^,,
ZHAO Wei-Qin

Institute of High Energy Physics, CAS, Beijing 100039,China2 China Center of Advanced Science and Technology, Beijing 100080, China

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Abstract：
The newly developed single trajectory quadrature method is applied to solve central potentials. First, based on the series expansion method an exact analytic solution of the ground state for Hulthen potential and an approximate solution for Yukawa potential are obtained respectively. Second, the newly developed iterative method based on Green function defined by quadratures along the single trajectory is applied to solve Yukawa potential using the Coulomb solution and Hulthen solution as the trial functions respectively. The results show that a more proper choice of the trial function will give a better convergence. To further improve the convergence the iterative method is combined with the variational method to solve the ground state wave function for Yukawa potential, using variational solutions of the Coulomb and Hulthen potentials as the trial functions. The results give much better convergence. Finally, the obtained critical screen coefficient is applied to discuss the dissociate temperature of J/ψ in high temperature QGP.

References

[1]	. Friedberg R ,Lee T D ,ZHAO W Q .Ann.Phys.,2001,288:522. Friedberg R ,Lee T D ,ZHAO W Q et al.Ann.Phys.,2001,293:13. Wong C Y .Introduction to High Energy Heavy Ion Collisions,World Scientific Pub.,344—356

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[2]	XIAO Jing,RUAN TuNan. Equations and Wave Functions of Integral Spin Particle. Chinese Physics C, 2000, 24(7): 631-635.
[3]	HAN Yong. Angular Momentum Projection of Cranked PNC Wave Function. Chinese Physics C, 2000, 24(6): 546-553.
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[6]	Wang Deyun,Huang Bowen. Solve for Energy Spectrum and Function of Ring-Shaped Oscillator by Using Supersymmetry and Shape Invariance. Chinese Physics C, 1999, 23(11): 1078-1082.
[7]	Huang Bowen,Wang Deyun. Energy Levels and Wavefunctions of Effective Screened Potential. Chinese Physics C, 1997, 21(8): 757-762.
[8]	Guo Hua,Wang Shunjin. Constrained Correlation Dynamics of QED in Canonical Form(Ⅰ) Equations of Motion for Correlation Green's Functions. Chinese Physics C, 1996, 20(1): 48-54.
[9]	Wang Shunjin,Guo Hua. Constrained Correlation Dynamics of SU(N) Gauge Theories in Canonical form (Ⅰ) Equations of Motion for Correlation Green's Functions. Chinese Physics C, 1995, 19(3): 270-277.
[10]	Zuo Wei,Guo Hua,Wang Shunjin. Dynamics of Many-Body Correlation Green's Functions Ⅳ. Relativistic Generalization. Chinese Physics C, 1994, 18(7): 616-620.
[11]	ZUO Wei,WANG Shun-Jin. Dynamics of Many-Body Correlation Green's Functions Ⅲ Truncation with Respect to Crder. Chinese Physics C, 1993, 17(2): 179-185.
[12]	LI Guang-Hua,HE Hui-Yong. Calculating on Wavefunctions of the Ground State Band for the Strong Coupling SU(3) Limit in IBM4. Chinese Physics C, 1992, 16(3): 278-284.
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[15]	WEI Hua,RUAN Tu-Nan. GREEN FUNCTION FOR RELATIVISTIC SCHRÖDINGER EQUATION. Chinese Physics C, 1986, 10(6): 656-665.
[16]	GOU Liang,HUANG Tao. PROTON DECAY RATE AND THE PROTON WAVEFUNCTION. Chinese Physics C, 1984, 8(1): 45-51.
[17]	SUN HONG-ZHOU,HAN QI-ZHI. THE CLASSIFICATION OF THE WAVE FUNCTIONS OF BOSONS AND FERMIONS. Chinese Physics C, 1982, 6(3): 317-322.
[18]	Yu You-wen,Wu Hui-fang. THE RELATIVISTIC DEUTERON WAVE FUNCTION. Chinese Physics C, 1980, 4(1): 1-7.
[19]	ZHOU GUANG-ZHAO,SU ZHAO-BING. RENORMALIZATION OF THE CLOSED TIME PATH GREEN'S FUNCTIONS IN NON-EQULIBRIUM STATISTICAL FIELD THEORY. Chinese Physics C, 1979, 3(3): 304-313.
[20]	WANG MING-CHUNG,CHENG HSI-THE,HSIEN TING-CHANG,WANG KE-LIN,CHANG CHENG-KANG. THE WAVE FUNCTION OF VECTOR MESON BOUND STATE THROUGH SCALAR COUPLING. Chinese Physics C, 1977, 1(1): 7-18.

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ZHANG Zhao and ZHAO Wei-Qin. Green Function Iterative Solution of Ground State Wave Function for Yukawa Potential[J]. Chinese Physics C, 2003, 27(3): 215-222.

ZHANG Zhao and ZHAO Wei-Qin. Green Function Iterative Solution of Ground State Wave Function for Yukawa Potential[J]. Chinese Physics C, 2003, 27(3): 215-222. shu

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Received: 2002-05-14
Revised: 1900-01-01

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沈阳化工大学材料科学与工程学院沈阳 110142

Green Function Iterative Solution of Ground State Wave Function for Yukawa Potential

ZHANG Zhao^,
ZHAO Wei-Qin

Corresponding author:ZHANG Zhao,

Institute of High Energy Physics, CAS, Beijing 100039,China2 China Center of Advanced Science and Technology, Beijing 100080, China

Received Date:2002-05-14
Accepted Date:1900-01-01
Available Online:2003-03-05

Abstract:The newly developed single trajectory quadrature method is applied to solve central potentials. First, based on the series expansion method an exact analytic solution of the ground state for Hulthen potential and an approximate solution for Yukawa potential are obtained respectively. Second, the newly developed iterative method based on Green function defined by quadratures along the single trajectory is applied to solve Yukawa potential using the Coulomb solution and Hulthen solution as the trial functions respectively. The results show that a more proper choice of the trial function will give a better convergence. To further improve the convergence the iterative method is combined with the variational method to solve the ground state wave function for Yukawa potential, using variational solutions of the Coulomb and Hulthen potentials as the trial functions. The results give much better convergence. Finally, the obtained critical screen coefficient is applied to discuss the dissociate temperature of J/ψ in high temperature QGP.