Related papers: Orthogonality and Boundary Conditions in Quantum M…
Quantum mechanics in the presence of $\delta$-function potentials is known to be plagued by UV divergencies which result from the singular nature of the potentials in question. The standard method for dealing with these divergencies is by…
This paper constructs relativistic quantum mechanical models of particles satisfying cluster properties and the spectral condition which do not conserve particle number. The treatment of particle production is limited to systems with a…
The energy functional, the governing partial differential equation(s) (PDE), and the boundary conditions need to be consistent with each other in a modeling system. In electrolyte solution study, people usually use a free energy form of an…
We study the possibility of supersymmetry (SUSY) in quantum mechanics in one dimension under the presence of a point singularity. The system considered is the free particle on a line R or on the interval [-l, l] where the point singularity…
We study the bound-state solutions of vanishing angular momentum in a quaternionic spherical square-well potential of finite depth. As in the standard quantum mechanics, such solutions occur for discrete values of energies. At first glance,…
Many-body quantum-mechanical stationary states that have real valued wavefunctions are shown to satisfy a classical conservation of energy equation with a kinetic energy function. The terms in the equation depend on the probability…
We consider a non-interacting gas under the inverted harmonic potential and present infinitely degenerate non-stationary orthogonal states. We discuss that it has an infinite entropy at the absolute zero temperature. We show that…
We postulate that physical states are equivalent under coordinate transformations. We then implement this equivalence principle first in the case of one-dimensional stationary systems showing that it leads to the quantum analogue of the…
Complicated boundary conditions are essential to accurately describe phenomena arising in nature and engineering. Recently, the investigation of a potential speedup through quantum algorithms in simulating the governing ordinary and partial…
Potential wells are employed to constrain quantum particles into forming discrete energy levels, acting as artificial few-level systems. In contrast, an anti-parity-time ($\mathcal{PT}$) symmetric system can have a single pair of real…
The fundamental principle of quantum mechanics is that the probabilities of physical outcomes are obtained from the intermediate states and processes of the interacting particles, considered as happening concurrently. When the interaction…
We exhibit an orthogonal set of product states of two three-state particles that nevertheless cannot be reliably distinguished by a pair of separated observers ignorant of which of the states has been presented to them, even if the…
At the lower edge of the energy continuum the birth of an isolated quantum bound state is studied as caused by an infinitesimally small change of the interaction. In our model a single, asymptotically free massive quantum particle is…
A quantum analog of the fundamental classical NOT gate is a quantum gate that would transform any input qubit state onto an orthogonal state. Intriguingly, this universal NOT gate is forbidden by the laws of quantum physics. This striking…
Statistical mechanics has grown without bounds in space. Statistical mechanics of point particles in an unbounded perfect gas is commonly accepted as a foundation for understanding many systems, including liquids like the concentrated salt…
The problem of boundary conditions in a supersymmetric theory of quantum cosmology is studied, with application to the one-loop prefactor in the quantum amplitude. Our background cosmological model is flat Euclidean space bounded by a…
Quantum multipartite entangled states play significant roles in quantum information processing. By using difference schemes and orthogonal partitions, we construct a series of infinite classes of irredundant mixed orthogonal arrays (IrMOAs)…
Firstly, a systematic procedure is derived for obtaining three-dimensional bound-state equations from four-dimensional ones. Unlike ``quasi-potential approaches'' this procedure does not involve the use of delta-function constraints on the…
The use of geometric methods has proved useful in the hamiltonian description of classical constrained systems. In this note we provide the first steps toward the description of the geometry of quantum constrained systems. We make use of…
In order to obtain a consistent formulation of octonionic quantum mechanics (OQM), we introduce left-right barred operators. Such operators enable us to find the translation rules between octonionic numbers and $8\times 8$ real matrices (a…