Abstract
The three-body problem is a famous question of mechanics. Newton actually quit physics because he found it too difficult. Henri Poincaré was the first to prove exact properties, and this contributed to his celebrity. The purpose of this chapter is to derive some rigorous results for the three-body problem in quantum mechanics. Here we are interested in obtaining rigorous lower bounds on three-body ground state energies. Upper bounds are easier to obtain by va iational calculations. We will see that our lower bounds are actually quite close to the exact answers, to which they provide useful approximations.
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References
J.-L. Basdevant, J.-M. Richard, and A. Martin, Nuclear Physics B343, 60, 69 (1990).
J-L. Basdevant, J.-M. Richard, A. Martin, and Tai Tsun Wu, Nuclear Physics B393, 111 (1993).
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© 2000 Springer-Verlag Berlin Heidelberg
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Basdevant, JL., Dalibard, J. (2000). Exact Results for the Three-Body Problem. In: The Quantum Mechanics Solver. Advanced Texts in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04277-9_9
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DOI: https://doi.org/10.1007/978-3-662-04277-9_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-04279-3
Online ISBN: 978-3-662-04277-9
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