Abstract
In suitable units, the Hamiltonian H for a free particle is the kinetic energy -½∇2 in ℝ3. For a system of N identical particles, it is -½∇2 in ℝn, with n = 3N. The Schrödinger Hamiltonian is obtained by adding a potential energy term. Self-adjoint versions of these operators are discussed in this chapter. In the case of just one particle (electron) in a Coulomb field (hydrogen-like atom), the relativistic (Dirac) Hamiltonian is also discussed.
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© 1978 Springer-Verlag New York Inc.
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Richtmyer, R.D. (1978). Some Partial Differential Operators of Quantum Mechanics. In: Principles of Advanced Mathematical Physics. Texts and Monographs in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46378-5_11
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DOI: https://doi.org/10.1007/978-3-642-46378-5_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-46380-8
Online ISBN: 978-3-642-46378-5
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