Quantum mechanics based on position

A. Dhahbi, YASSINE CHARGUI, Adel Trablesi

The study of physical systems endowed with a position-dependent mass (PDM) remains a fundamental issue of quantum mechanics. In this paper we use a new approach, recently developed by us for building the quantum kinetic energy operator (KEO) within the Schrodinger equation, in order to construct a new class of exactly solvable models with a position varying mass, presenting a harmonic-oscillator-like spectrum. To do so we utilize the formalism of supersymmetric quantum mechanics (SUSY QM) along with the shape invariance condition. Recent outcomes of non-Hermitian quantum mechanics are also taken into account.

C. Vargas‐Hernández

Spiros Konstantogiannis

Making an intuitive assumption, and using the completeness of the position and momentum eigenstates, along with the postulates of quantum mechanics, we provide a geometric presentation of the position and momentum representations in quantum mechanics, in the hope of offering a perspective complementary to those given in standard textbooks.

Fernando Sansò, Federica Migliaccio

M. Dean Johnson

Mathematics (Option 1) with a minor in Physics. In his sophomore year, he participated in the studentfaculty colloquium, where he explored quantum computing with several other students and faculty. Quantum mechanics is a scientific theory that seeks to describe atomic and subatomic particles (or quantum particles) as well as the interaction among them. Such particles include electrons, protons, neutrons, and photons. In classical mechanics, a particle’s future state is described with certainty once its present state is known. At any given moment, its momentum and position are determined with certainty. In quantum mechanics, its future state is described probabilistically. Instead of a single momentum, a particle can assume a simultaneous range of momenta, and instead of a single position, it can take a simultaneous range of positions. Since the product of these ranges is no less than a specific positive universal constant, a decrease in the range of its position forces an increase in the range of momentum and vice versa. It