Solution of Time-Dependent Coulomb Potential with Linear Potential

SONG Xiao-Hui; YANG Xin-E; WANG Ping

Chinese Physics C> 2003, Vol. 27> Issue(9) : 775-778

Solution of Time-Dependent Coulomb Potential with Linear Potential

School of Science, Department of Applied Physics, Tianjin University, Tianjin 300072, China2 LiuHui Center for Applied Mathematics, Nankai University & Tianjin University, Tianjin 300072, China

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Abstract：
In this paper, we make use of the Burgan et al's method to derive the solution of the time dependent coulomb potential and linear potential with a special form, V(r,t)=-a0ξ 12r+a 1rξ32, (where ξ=at 2+bt+c, a 0, a 1, a,b,c are parameters with certain relations) and furthermore we discussed the wave function for V(r,t)=-a 0ξ 12r+nk=1 a kr kξ k2+1 (where a 0, a 1, ..., a n are constants), Meanwhile we analyzed the physical meaning of this special potential and the importance of the linear scaling factors C(t) in the study of repeated elastic reflections of a particle in an expanding spherical cavity.

References

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. Burgen J R ,Fiex M R ,Fijalkow E et al.Phys.Lett.,1979,74A(1,2):112. Guedes I.Phys.Rev.,2001,63A(3):0341023. Lewis Jr.H R ,Riesenfeld W B .J .Math.Phys.,1969,10:1458 4. SongDaeYup.Phys.Rev.,2000,62A(1):014103 5. John R .Ray.Phys.Rev.,1982,A28(8):729 6. de Souza C Farina,de Souza Dutra A .Phys.Lett.,1987,A123(6):297 7. Flessas G P ,Das K .Phys.Lett.,1980,A78(1):198. Eichten E et al.Phys.Rev.,1978,D17:3090;Phys.Rev.,1980,D21:2039. LIU Bo,SHEN Peng-Nian,JIANG Huan-Qing.HEP NP ,1998,22(6):556(in Chinese)(刘波,沈彭年,姜焕清.高能物理与核物理,1998,22(6):556)10. Berry M V ,Klein G .J.Phys.,1984,A17:1805

[1] CHANG KONG-LIANG . DIMENSIONAL METHOD TO SOLVE THE DIFFUSION CONVECTION EQUATION OF SOLAR COSMIC RAYS. Chinese Physics C, 1978, 2(3): 200-210.
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SONG Xiao-Hui, YANG Xin-E and WANG Ping. Solution of Time-Dependent Coulomb Potential with Linear Potential[J]. Chinese Physics C, 2003, 27(9): 775-778.

SONG Xiao-Hui, YANG Xin-E and WANG Ping. Solution of Time-Dependent Coulomb Potential with Linear Potential[J]. Chinese Physics C, 2003, 27(9): 775-778. shu

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Received: 2003-01-20
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

Solution of Time-Dependent Coulomb Potential with Linear Potential

Corresponding author: YANG Xin-E,

School of Science, Department of Applied Physics, Tianjin University, Tianjin 300072, China2 LiuHui Center for Applied Mathematics, Nankai University & Tianjin University, Tianjin 300072, China

Received Date: 2003-01-20
Accepted Date: 1900-01-01
Available Online: 2003-09-05

Abstract: In this paper, we make use of the Burgan et al's method to derive the solution of the time dependent coulomb potential and linear potential with a special form, V(r,t)=-a0ξ 12r+a 1rξ32, (where ξ=at 2+bt+c, a 0, a 1, a,b,c are parameters with certain relations) and furthermore we discussed the wave function for V(r,t)=-a 0ξ 12r+nk=1 a kr kξ k2+1 (where a 0, a 1, ..., a n are constants), Meanwhile we analyzed the physical meaning of this special potential and the importance of the linear scaling factors C(t) in the study of repeated elastic reflections of a particle in an expanding spherical cavity.