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Abstract

The Hamiltonian for two interacting particles is, as known
$$\hat H = - \frac{{{\hbar ^2}}}{{2{m_1}}}{\Delta _1} - \frac{{{\hbar ^2}}}{{2{m_2}}}{\Delta _2} + V({\vec r_1},{\text{ }}{\vec r_2}),$$
(1.1)
where
$${\Delta _1} \equiv \nabla _1^2 = \frac{{{\partial ^2}}}{{\partial x_1^2}} + \frac{{{\partial ^2}}}{{\partial y_1^2}} + \frac{{{\partial ^2}}}{{\partial z_1^2}}$$
(1.2)
and Δ2 is analogously defined. In a closed system the potential energy V depends only on the relative position of the particles, so we may write
$$\hat H = - \frac{{{\hbar ^2}}}{{2{m_1}}}{\Delta _1} - \frac{{{\hbar ^2}}}{{2{m_2}}}{\Delta _2} + V({\vec r_1} - {\vec r_2}).$$
(1.3)

Keywords

Wave Function Coupling Term Electronic Wave Function Schrodinger Equation Free Atom 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • István Mayer
    • 1
  1. 1.Chemical Research CenterHungarian Academy of SciencesBudapestHungary

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