Related papers: Classification Scheme for Kinetic Energy Operators…
These short notes present to the reader (students, in particular) a concise approach to the derivation of the propagator of Hamiltonians with position-dependent kinetic energy. The formalism is applied to the von Roos Hamiltonian with…
Noncommutivity of position and momentum makes it difficult to formulate the unambiguous structure of the kinetic part of Hamiltonian for the position-dependent effective mass (PDEM). Various existing proposals of writing the viable kinetic…
In this work, we analyze a particle with position-dependent mass, with solitonic mass distribution in a stationary quantum system, for the particular case of the BenDaniel-Duke ordering, in a hyperbolic barrier potential. The kinetic energy…
Cylindrically symmetric quantum mechanical systems with position dependent masses (PDM) admitting at least one second order integral of motion are classified. It is proved that there exist 68 such systems which are inequivalent. Among them…
Ordered chains (such as chains of amino acids) are ubiquitous in biological cells, and these chains perform specific functions contingent on the sequence of their components. Using the existence and general properties of such sequences as a…
We consider the modified Emden equation (MEE) and introduce its most general solution, using the most general solution for the simple harmonic oscillator's linear dynamical equation (i.e., the initial conditions shall be identified by the…
The design of optimization algorithms for neural networks remains a critical challenge, with most existing methods relying on heuristic adaptations of gradient-based approaches. This paper introduces KO (Kinetics-inspired Optimizer), a…
The exact solvability and impressive pedagogical implementation of the harmonic oscillator creation and annihilation operators make it a problem of great physical relevance and the most fundamental one in quantum mechanics. So would be the…
A Hermitian and an anti-Hermitian first-order intertwining operators are introduced and a class of $\eta$-weak-pseudo-Hermitian position-dependent mass (PDM) Hamiltonians are constructed. A corresponding reference-target…
We analyze two simple models derived from a quantum-mechanical particle on an elliptical path. The first Hamiltonian operator is non-Hermitian but equivalent to an Hermitian operator. It appears to exhibit the same two-fold degeneracy as…
Within ``orbital-free'' density functional theory, it is essential to develop general kinetic energy density (KED), denoted as $t(\mathbf{r})$. This is usually done by empirical corrections and enhancements, gradient expansions, machine…
For relativistic closed systems, an operator is explained which has as stationary eigenvalues the squares of the total cms energies, while the wave function has only half as many components as the corresponding Dirac wave function. The…
We present a new framework for optimal and feedback control of PDEs using Koopman operator-based reduced order models (K-ROMs). The Koopman operator is a linear but infinite-dimensional operator which describes the dynamics of observables.…
We present a reduced density operator for electronically open molecules by explicitly averaging over the environmental degrees of freedom of the composite Hamiltonian. Specifically, we include the particle-number non-conserving…
We study the performance of fourth-order gradient expansions of the kinetic energy density (KED) in semi-local kinetic energy functionals depending on the density-dependent variables. The formal fourth-order expansion is convergent for…
The well known and oft-quoted Feynman's expression, entered the title, leading at a loss and even being objectionable, has not yet a clear explanation. The hidden parameters problem in quantum mechanics is considered here on the base of…
An axiomatic approach is herein used to determine the physically acceptable forms for general $D$-dimensional kinetic energy density functionals (KEDF). The resulted expansion captures most of the known forms of one-point KEDFs. By…
Let V be a linear subspace of M_n(C) which contains the identity matrix and is stable under the formation of Hermitian adjoints. We prove that if n is sufficiently large then there exists a rank k orthogonal projection P such that dim(PVP)…
We introduce the notion of a $k$-mode weakly stationary quantum process $\varrho$ based on the canonical Schr\"odinger pairs of position and momentum observables in copies of $L^2(\mathbb{R}^k)$, indexed by an additive abelian group $D$ of…
Collective many-body dynamics for time-dependent quantum Hamiltonian functions is investigated for a dynamical system that exhibits multiple degrees of freedom, in this case a combined (Paul and Penning) trap. Quantum stability is…