Thiemann T, Rodriguez Zarate A (2026)
Publication Type: Journal article
Publication year: 2026
Book Volume: 101
Article Number: 225213
Journal Issue: 22
Interesting quantum integrable models are rare and one often has to resort to approximation methods. One of these is the Rayleigh Ritz method which under certain circumstances allows to approximately compute the lowest energy eigenstate (or ground state) of a given Hamiltonian whose pure point spectrum is bounded from below. The quality of such approximations can then be tested numerically or sometimes by abstract arguments. However, the numerical test is limited by computing power. In order to perform a rigorous test, one would need to have at one’s disposal 1. a physically interesting model that is 2. solvable to sufficient extent in order that 3. the exact ground state is known in closed form. In this contribution we show that certain anharmonic potentials of the Mexican hat type belong to this class of models. The corresponding Schrödinger type Hamiltonian can be considered as a crude quantum mechanical toy model Hamiltonian for the Higgs field in the standard model of elementary particle physics.
APA:
Thiemann, T., & Rodriguez Zarate, A. (2026). Rigorous test of the Raleigh-Ritz method for Mexican hat type potentials. Physica Scripta, 101(22). https://doi.org/10.1088/1402-4896/ae6b11
MLA:
Thiemann, Thomas, and Anniela Rodriguez Zarate. "Rigorous test of the Raleigh-Ritz method for Mexican hat type potentials." Physica Scripta 101.22 (2026).
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