Abstract
This section is recorded by MIPT student Sharipov Rustem. It contains the derivation of the properties of the Hermite polynomials and their application to quantum mechanics and representation theory.
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Similarly \((\cosh {t},\sinh {t})\) solves the equation \(\frac{d^2 u(t)}{dt^2}=u(t)\) and provides the representation of the SO(1, 1) algebra—the algebra of Lorentz transformations in the two-dimensional Minkowski space-time.
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Akhmedova, V., Akhmedov, E.T. (2019). Hermite Polynomials. In: Selected Special Functions for Fundamental Physics. SpringerBriefs in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-35089-5_4
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DOI: https://doi.org/10.1007/978-3-030-35089-5_4
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