Abstract
The Schrödinger–Pauli theory is characterized by the fact that every system must have a ground state, whose energy is a lower bound to the energies of all states. This is not true in Classical Mechanics, in which, for instance, a H atom could have any energy.
Variational principles are ubiquitous in Theoretical Physics and are very useful mathematical tools. This one depends on the existence of a ground state.
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Notes
- 1.
A functional of \(\phi \) is an integral that has \(\phi \) in the integrand; it can be considered as a function of infinitely many variables, which are the values taken by \(\phi \) in the field of integration. This one is quadratic, since \(\phi \) appears in bra and ket.
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Cini, M. (2018). Variational Principle for Schrödinger–Pauli Theory . In: Elements of Classical and Quantum Physics. UNITEXT for Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-71330-4_21
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DOI: https://doi.org/10.1007/978-3-319-71330-4_21
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