The infinite square well and the attractive Dirac delta function potentials are arguably two of
the most widely used models of one-dimensional bound-state systems in quantum …

Quantum transients are temporary features of matter waves before they reach a stationary
regime. Transients may arise after the preparation of an unstable initial state or due to a …

We consider transmission and reflection of narrow Gaussian wave packets by delta
potentials in the cases of constant and specific (inverse linear) time-dependent strength …

We provide simple examples of closed-form Gaussian wave packet solutions of the free-
particle Schrödinger equation in one dimension which exhibit the most general form of the …

Recently, general point interactions in one dimension has been used to model a large
number of different phenomena in quantum mechanics. Such potentials, however, require …

We consider time-dependent Gaussian wave packet solutions of the Schrödinger equation,
with arbitrary initial central position, x 0, and momentum, p 0, for an otherwise free particle …

We give examples of “shrinking” free wave packets with zero initial velocity in one
dimension. Considering different measures of spatial extension of wave packets, we show …

Here we study a one-dimensional finite lattice formed by generalized contact interactions in
a circular setup, ie, under periodic boundary conditions. Considering only four such …

We derive expressions for polynomials governing the threshold conditions for different types
of locally periodic Dirac comb potentials comprising of attractive and combination of …

The Schrödinger equation is solved for the case of a particle confined to a small region of a
box with infinite walls. If the walls of the well are moved, then, due to an effective quantum …