English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The problem of construction of a simple one - dimensional Hamiltonian whosespectrum coincides with the set of primes is considered. We note thatquasiclassically a Hamiltonian whose spectrum has the same counting function asthat of the primes in the leading order (i. e. integral logarithm) can beconstructed with the function V(x) whose inverse is asymptotically given byx=li(V^(1/2)). Hamiltonians, whose spectra coincide with the first 1 - 1000primes are constructed numerically and their fractal structure is revealed. Thepossibility of using such a "prime-generating" Hamiltonian for investigation ofcertain number-theoretical problems is discussed.

On the Hamiltonian whose spectrum coincides with the set of primes