On the Hamiltonian whose spectrum coincides with the set of primes

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dc.creatorSekatskii, Sergey K.
dc.date2007-09-04
dc.date.accessioned2026-07-07T08:27:26Z
dc.date.available2026-07-07T08:27:26Z
dc.descriptionThe problem of construction of a simple one - dimensional Hamiltonian whose spectrum coincides with the set of primes is considered. We note that quasiclassically a Hamiltonian whose spectrum has the same counting function as that of the primes in the leading order (i. e. integral logarithm) can be constructed with the function V(x) whose inverse is asymptotically given by x=li(V^(1/2)). Hamiltonians, whose spectra coincide with the first 1 - 1000 primes are constructed numerically and their fractal structure is revealed. The possibility of using such a "prime-generating" Hamiltonian for investigation of certain number-theoretical problems is discussed.
dc.identifierhttps://arxiv.org/abs/0709.0364
dc.identifierhttp://arxiv.org/abs/0709.0364
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/137272
dc.subjectMathematical Physics
dc.titleOn the Hamiltonian whose spectrum coincides with the set of primes
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