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The Investigation and Study of Hydrogen Atom in Spherical Cavity Using B-Spline Basis Functions: A Mathematical Approach

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A. Heidari, F. Jahromi, R. Amiri and M. Ghorbani, "The Investigation and Study of Hydrogen Atom in Spherical Cavity Using B-Spline Basis Functions: A Mathematical Approach,"

*Journal of Modern Physics*, Vol. 3 No. 4, 2012, pp. 334-339. doi: 10.4236/jmp.2012.34045.

[1] | V. K. Dolmatov, A. S. Baltenkov, J.-P. Connerade and S. T. Manson, “Structure and Photoionization of Confined Atoms,” Radiation Physics and Chemistry, Vol. 70, No. 1-3, 2004, pp. 417-433. doi:10.1016/j.radphyschem.2003.12.024 |

[2] | A. Michels, J. Deboer and A. Bijl, “Remarks Concerning Molecural Interaction and Their Influence on the Polarisability,” Physica, Vol. 4, 1937, pp. 981-994. doi:10.1016/S0031-8914(37)80196-2 |

[3] | S. Kang, Q. Liu, H. Y. Meng and T. Y. Shi, “Hydrogen Atom in Ellipsoidal Cavity,” Physics Letters A, Vol. 360, No. 4-5, 2007, pp. 608-614. doi:10.1016/j.physleta.2006.08.055 |

[4] | S. H. Patil, “Hydrogen Atom Confined to an Ellipsoid,” Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 34, No. 6, 2001, p. 1049. doi:10.1088/0953-4075/34/6/306 |

[5] | T. Guillot, “A Comparison of the Interiors of Jupiter and Saturn,” Planetary and Space Science, Vol. 47, No. 10-11, 1999, pp. 1183-11200. doi:10.1016/S0032-0633(99)00043-4 |

[6] | T. Y. Shi, H. X. Qiao and B. W. Li, “Variational Calculations for a Hydrogen Atom Confined Off-Centre in an Impenetrable Spherical Box Using B-Splines,” Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 33, No. 9, 2000, p. L349. doi:10.1088/0953-4075/33/9/106 |

[7] | H. Bachau, E. Cormier, P. Decleva, J. E. Hansen and F. Martín, “Applications of B-Splines in Atomic and Molecular Physics,” Reports on Progress in Physics, Vol. 64, No. 12, 2001, p. 1815. doi:10.1088/00344885/64/12/205. |

[8] | W. R. Johnson and J. Sapirstein, “Computation of Second-Order Many-Body Corrections in Relativistic Atomic Systems,” Physical Review Letters, Vol. 57, No. 9, 1986, pp. 1126-1129. doi:10.1103/PhysRevLett.57.1126 |

[9] | D. A. Horner, S. Miyabe, T. N. Rescigno, C. W. McCurdy, F. Morales and F. Martín, “Classical Two-Slit Interference Effects in Double Photoionization of Molecular Hydrogen at High Energies,” Physical Review Letters, Vol. 101, No. 18, 2008, pp. 183002-183005. doi:10.1103/PhysRevLett.101.183002 |

[10] | D. A. Horner, C. W. McCurdy and T. N. Rescigno, “Triple Differential Cross Sections and Nuclear Recoil in Two-Photon Double Ionization of Helium,” Physical Review A, Vol. 78, No. 4, 2008, Article ID 04341. doi:10.1103/PhysRevA.78.043416 |

[11] | A. Palacios, T. N. Rescigno and C. W. McCurdy, “Cross Sections for Short-Pulse Single and Double Ionization of Helium,” Physical Review A, Vol. 77, No. 3, 2008, Article ID 032716. |

[12] | F. L. Yip, C. W. McCurdy and T. N. Rescigno, “Hybrid Gaussian-Discrete-Variable Representation Approach to Molecular Continuum Processes: Application to Photoionization of Diatomic Li2+,” Physical Review A, Vol. 78, No. 2, 2008, Article ID 023405. doi:10.1103/PhysRevA.78.023405 |

[13] | P. L. Bartlett, A. T. Stelbovics, T. N. Rescigno and C. W. McCurdy, “Application of Exterior Complex Scaling to Positron-Hydrogen Collisions including Rearrangement,” Physical Review A, Vol. 77, No. 3, 2008, Article ID 032710. doi:10.1103/PhysRevA.77.032710 |

[14] | D. A. Horner, W. Vanroose, T. N. Rescigno, F. Martin and C. W. McCurdy, “The Role of Nuclear Motion in the Photo-Double Ionization of Molecular Hydrogen,” Lawrence Berkeley National Laboratory, Paper LBNL-61189, 2008. |

[15] | J. C. Morrison and C. Bottcher, “Spline Collocation Methods for Calculating Orbital Energies,” Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 26, No. 22, 1993, pp. 3999-4006. doi:10.1088/0953-4075/26/22/007. |

[16] | W. R. Johnson, S. A. Blundell and J. Sapirstein, “Finite Basis Sets for the Dirac Equation Constructed from B Splines,” Physical Review A, Vol. 37, No. 2, 1988, pp. 307-315. doi:10.1103/PhysRevA.37.307 |

[17] | W. R. Johnson, S. A. Blundell and J. Sapirstein, “Many-Body Perturbation-Theory Calculations of Energy Levels along the Lithium Isoelectronic Sequence,” Physical Review A, Vol. 37, No. 8, 1988, pp. 2764-2777. doi:10.1103/PhysRevA.37.2764 |

[18] | W. R. Johnson, S. A. Blundell and J. Sapirstein, “Many-Body Perturbation-Theory Calculations of Energy Levels along the Sodium Isoelectronic Sequence,” Physical Re- view A, Vol. 38, No. 6, 1988, pp. 2699-2706. doi:10.1103/PhysRevA.38.2699 |

[19] | W. R. Johnson, S. A. Blundell, Z. W. Liu and J. Sapirstein, “Correlation Effects in the Parity-Noncomserving 6s→7s Transition in Cesium,” Physical Review A, Vol. 37, 1988, pp. 1395-1400. doi:10.1103/PhysRevA.37.1395 |

[20] | S. A. Blundell, W. R. Johnson and J. Sapirstein, “Higher-Order Many-Body Perturbation-Theory Calculations of Energy Levels in Cesium,” Physical Review A, Vol. 38, No. 10, 1988, pp. 4961-4966. doi:10.1103/PhysRevA.38.4961 |

[21] | T. K. Fang and T. N. Chang, “Photoionization from Excited Mg Atoms,” Physical Review A, Vol. 61, No. 5, 2000, Article ID 052716. doi:10.1103/PhysRevA.61.052716 |

[22] | T. K. Fang and T. N. Chang, “B-Spline-Based Multichan-Nel K-Matrix Method for Atomic Photoionization,” Physical Review A, Vol. 61, No. 6, 2000, Article ID 062704. doi:10.1103/PhysRevA.61.062704 |

[23] | C. W. McCurdy and F. Martin, “Implementation of Exterior Complex Scaling in B-Splines to Solve Atomic and Molecular Collision Problems,” Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 37, No. 4, 2004, p. 917. doi:10.1088/0953-4075/37/4/017 |

[24] | B. Nine, O. Haif-Khaif and A. Zerarka, “The Eigenenergies of the Wave Function through the Non-Variational Galerkin-B-Spline Approach,” Applied Mathematics and Computation, Vol. 178, No. 2, 2006, pp. 486-492. doi:10.1016/j.amc.2005.11.067 |

[25] | N. Aquino, G. Campoy and H. E. Montgomery Jr., “Highly Accurate Solutions for the Confined Hydrogen Atom,” International Journal of Quantum Chemistry, Vol. 107, No. 7, 2007, pp. 1548-1558. doi:10.1002/qua.21313 |

[26] | S. Goldman and C. Joslin, “Spectroscopic Properties of an Isotropically Compressed Hydrogen Atom,” Journal of Physical Chemistry, Vol. 96, No. 14, 1992, pp. 6021-6027. doi:10.1021/j100193a069 |

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