11 citations · 63 across the 21 of their papers we have counts for
22 papers
A Note on the Measure of Vector and Pythagorean Theorem
Yu. V. Brezhnev
Why the square? We present a geometry-axiom-free derivation of the Pythagorean theorem and the square at its core, establishing their algebraic origin from within the bare vector-s…
Why and whence the Hilbert space in quantum theory?
Yu. V. Brezhnev
We explain why and how the Hilbert space comes about in quantum theory. The axiomatic structures of vector space, of scalar product, of orthogonality, and of the linear functional…
An exactly solvable problem of wave fronts and applications to the asymptotic theory
Yu. Brezhnev, A. Tsvetkova
This is the full and extended version of the brief note arXiv:1908.00938. A nontrivially solvable 4-dimensional Hamiltonian system is applied to the problem of wave fronts and to t…
On Hamiltonian systems integrable in elliptic functions that describe waves over underwater banks and ridges
Yu. Brezhnev, A. Tsvetkova
We discuss the 4-dimensional Hamiltonian systems that describe waves over underwater banks and ridges. The systems are exactly integrable in terms of elliptic functions and of solu…
The Born rule
Yurii V. Brezhnev
We deduce the Born rule. No use is required of quantum postulates. One exploits only rudimentary quantum mathematics--a linear, not Hilbert', vector space--and empirical notion of…
Linear superposition as a core theorem of quantum empiricism
Yurii V. Brezhnev
Clarifying the nature of the quantum state is at the root of the problems with insight into counter-intuitive quantum postulates. We provide a direct-and math-axiom fre…