Abstract
This section presents an approximate calculation of the energy levels for the helium atom as shown in [F171, problem 90]. We make use of a pure Coulomb Hamiltonian, i.e., no spin-dependent forces are included. The wavefunction separates into a spin part and a spatial part. We cannot ignore the spin part, however, as the requirement of an anti-symmetric (AS) two-electron wavefunction (Pauli principle) has to be satisfied. The wavefunction is given as a product of the coordinate space part that can be chosen to be symmetric (S), ψ S, or AS, ψ AS, under particle interchange times a two-particle spinor that again can be either S or AS, labeled χS and χAS, respectively. Thus, we can have an overall AS combination ψ S × χAS or ψ AS × χS.
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© 1995 Springer-Verlag Berlin Heidelberg
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Horbatsch, M. (1995). Many-Particle Problems. In: Quantum Mechanics Using Maple®. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79538-1_7
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DOI: https://doi.org/10.1007/978-3-642-79538-1_7
Publisher Name: Springer, Berlin, Heidelberg
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Online ISBN: 978-3-642-79538-1
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