A bstract We compare the path integral for transition functions in unimodular gravity and general relativity. In cosmological constant is a property of states that are specified at boundaries whereas relativity parameter action. Unimodular with nondynamical background spacetime volume element has time variable canonically conjugate to constant. Wave depend on satisfy Schrödinger equation. On co...

(Abstract) The ordinary Schrödinger equation with minimal coupling for a nonrelativistic electron interacting with a single-mode photon field is not satisfied by the nonrelativistic limit of the exact solutions to the corresponding Dirac equation. A Schrödinger-like equation valid for arbitrary photon intensity is derived from the Dirac equation without the weak-field assumption. The ”eigenvalu...

One of the greatest scientific achievements of physics in the 20th century is the discovery of quantum mechanics. The Schrödinger equation is the most fundamental equation in quantum mechanics describing the time-based evolution of the quantum state of a physical system. It has been found that the time-independent version of the equation can be derived from a general optimization algorithm. Ins...

in oneand two-channel central potentials Abstract Quantum scattering theory aims to model the interactions of particles in the quantum regime as the particles scatter from one another. The theoretical understanding of these events often necessitates solutions to the time-independent Schrödinger equation. For computational purposes, it becomes necessary to limit consideration of a scattering eve...

Abstract A previous study by Mantas and Vecil (Int J High Perform Comput Appl 34(1): 81–102, 2019) describes an efficient accurate solver for nanoscale DG MOSFETs through a deterministic Boltzmann-Schrödinger-Poisson model with seven electron–phonon scattering mechanisms on hybrid parallel CPU/GPU platform. The transport computational phase, i.e. the time integration of Boltzmann equations, was...

Abstract. This chapter is a review of the research of the authors from the last decade and focuses on the mathematical analysis of the Schrödinger model for nano–scale semiconductor devices. We discuss transparent boundary conditions (TBCs) for the time–dependent Schrödinger equation on a two dimensional domain. First we derive the two dimensional discrete TBCs in conjunction with a conservativ...

Small-amplitude excitations in a deformable discrete nonlinear Schrödinger equation. A detailed analysis of the small-amplitude solutions of a deformed discrete nonlin-ear Schrödinger equation is performed. For generic deformations the system possesses " singular " points which split the infinite chain in a number of independent segments. We show that small-amplitude dark solitons in the vicini...