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Atomic Systems

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Quantum Mathematical Physics

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Abstract

The quantum-mechanical treatment of the problem of two particles interacting through a 1 /r potential follows the outlines of the classical theory (I: §4.2). It starts with the Hamiltonian

$$H = \frac{{|{P_1}{|^2}}}{{2{m_1}}} + \frac{{|{P_2}{|^2}}}{{2{m_2}}} + \frac{\alpha }{{|{X_1} - {X_2}|}},\alpha = {e_1}{e_2},$$
(4.1)

which acts a priori on H = H 1 ⊗ H 2, where H i , is the Hilbert space of the i-th particle. The system can be decomposed into two independent parts by the

The hydrogen atom is so simple that a complete mathematical analysis can be made. This analysis was a watershed of atomic physics.

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  1. Institute for Theoretical Physics, University of Vienna, Boltzmanngasse 5, 1090, Vienna, Austria

    Walter Thirring

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Thirring, W. (2002). Atomic Systems. In: Quantum Mathematical Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05008-8_4

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