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Pramana

, Volume 26, Issue 6, pp 481–487 | Cite as

One-parameter Lie groups admitted by time-dependent Schrödinger equation: Atoms, molecules and nucleons in harmonic oscillator field

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Abstract

Lie’s method of differential equation is used to obtain the one-parameter Lie groups admitted by the time-dependent Schrödinger equations for atoms, molecules and nucleons in harmonic oscillator field. This group for atoms and molecules is isomorphic to 10-parameter inhomogeneous orthogonal group in 4 dimensions, irrespective of the numbers of nuclei and electrons. For Z protons andN neutrons in a harmonic oscillator field, both isotropic and anisotropic, the r-parameter Lie groups are seraidirect products of an invariant subgroup and a factor group. In the case of isotropic oscillator field r is 1/2[3Z(3Z-1) +3N (3N -1)+2], while for the anisotropic oscillator field r is 1/2[3Z (Z+1)+3N(JV+1)+2].

Keywords

One-parameter Lie groups atoms molecules harmonic oscillator field 

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Copyright information

© Indian Academy of Sciences 1986

Authors and Affiliations

  • P Rudra
    • 1
  1. 1.Department of PhysicsUniversity of KalyaniKalyaniIndia

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