Abstract
The quantum oscillator (QO) is the quantum-mechanical analog of the classical harmonic oscillator. An arbitrary potential can usually be approximated as a harmonic potential at the vicinity of a stable equilibrium point. Then the QO can be used as the important model systems in quantum mechanics. It is one of the few quantum-mechanical systems for which an exact, analytical solution is known from the Schrödinger equation (SE). Here, we consider the QO behavior on the basement the unified non-local theory (UNLT), compare results with Madelung’s hydrodynamics and apply the UNLT to transport processes in the much more complicated physical systems like graphene. The origin of the charge density waves (CDWs) is a long-standing problem relevant to a number of important issues in condensed matter physics. Mathematical modeling of the CDW expansion as well as the problem of the high-temperature superconducting can be solved only on the basement of the non-local quantum hydrodynamics.
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