Upon revisiting the Hamiltonian structure of classical wavefunctions in Koopman–von
Neumann theory, this paper addresses the long-standing problem of formulating a …

This paper proposes a method for constructing exactly solvable time-dependent oscillator
families based on the invariant operator method and the duality method. An exactly solvable …

The longstanding question of how stochastic behaviour arises from deterministic
Hamiltonian dynamics is of great importance, and any truly holistic theory must be capable …

Several quantum gravity and string theory thought experiments indicate that the Heisenberg
uncertainty relations get modified at the Planck scale so that a minimal length do arises. This …

This contribution has two main purposes. First, using classical optics we show how to model
two coupled quantum harmonic oscillators and two interacting quantized fields. Second, we …

We use the Hilbert space formulation of classical mechanics, known as the Koopman–von
Neumann formalism, to study adiabatic driving, geometric phases, and the geometric tensor …

In the context of quantum dynamics there exists a coordinate transformation which maps the
free particle to the harmonic oscillator. Here we extend this result by reformulating it as a …

We construct an operational formulation of classical mechanics without presupposing
previous results from analytical mechanics. In doing so, we rediscover several results from …

We study the evolution of the energy of a harmonic oscillator when its frequency slowly
varies with time and passes through a zero value. We consider both the classical and …

Abstract In the paper (Ramos-Prieto et al., Sci. Rep. 8, 8401 2018), among other things, the
Ermakov-Lewis invariant was constructed for the time dependent harmonic oscillator in …