A characterization of the Hamiltonian |
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Authors: | Franciszek Hugon Szafraniec |
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Institution: | Instytut Matematyki, Uniwersytet Jagiellońiski ul. Reymonta 4, PL-30059 Kraków, Poland |
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Abstract: | The classical Hamiltonian ) of the very classical quantum harmonic oscillator, which is regarded as a germ of the most of what comes about in quantum mechanics, can be sublimed to an abstract operator in a separable Hilbert space. Having this done one may ask for a condition which would allow it to be identified among operators of a suitable class. This class is that corresponding to three diagonal matrices and the property which makes the action successful is a kind of diagonal invariance (up to change of basis) within the class in question. |
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Keywords: | unbounded operator self-adjoint operator Jacobi (matrix) operator abstract Hamiltonian Hermite polynomials Charlier polynomials |
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