The Structure of the Atom and Its Interaction with an Electromagnetic Field

  • M. Ya. Amusia
Part of the Physics of Atoms and Molecules book series (PAMO)


The Hamiltonian of an atom composed of a nucleus (of charge Z) and N electrons consists of three summations: these are sums over the kinetic and potential energy operators for each separate electron moving in the field of the nucleus and also over the interelectronic Coulomb interaction terms:
$$ \widehat H = \sum\limits_{n = 1}^N {\left( {\frac{{\widehat p_n^2}}{2} - \frac{Z}{{{r_n}}}} \right)} + \frac{1}{2}\sum\limits_{n > q = 1}^N {\frac{1}{{\left| {{r_n} - {r_q}} \right|}}} ,{\widehat p_n} = - i{\nabla _n} = - i\frac{\partial }{{\partial {r_n}}} $$
where r n is the radius vector of the nth electron. For a neutral atom N = Z. In (2.1) all relativistic effects have been neglected so all interactions represented are of Coulombic origin. The state of an atom is determined by its wavefunction Ψ E (x 1x N ), which is a solution of the stationary Schrödinger equation:
$$\hat{H}\Psi_E(x_1\cdot\cdot\cdot x_N)=E\Psi_E(x_1\cdot\cdot\cdot x_N)$$
where Ψ E depends on the spatial coordinates and spin projection of each electron, i.e., x n r n , σ n .


Orbital Angular Momentum Schrodinger Equation Principal Quantum Number Atomic Electron Photoionization Cross Section 
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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • M. Ya. Amusia
    • 1
  1. 1.A. F. Ioffe Physicotechnical InstituteAcademy of Sciences of the USSRLeningradUSSR

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