Solution of Time-Dependent Coulomb Potential with Linear Potential

  • 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.
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  • [1] . 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
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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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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

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.

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