The Energy Spectrum of Harmonium

Cyrnek, Lech

doi:10.1142/9789812704474_0032

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2003

2023

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Cited by 4 publications

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Harmonium

Karwowski¹,

Cyrnek²

2004

Annalen der Physik

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The eigenvalue problem of a Hamiltonian describing two interacting particles confined by an external harmonic‐oscillator potential is analyzed. If the particles are identical, the system is referred to as harmonium. Harmonium belongs to very few non‐trivial two‐particle systems for which the Schrödinger equation is not only separable but also, for several interaction potentials and for a set of the coupling constants, quasi‐exactly solvable. In particular, the complete spectrum of harmonium has been obtained and analyzed. Also some aspects or relativistic generalizations of the model are briefly discussed.

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