As early as 1902, Gibbs pointed out that systems whose partition function diverges, eg
gravitation, lie outside the validity of the Boltzmann–Gibbs (BG) theory. Consistently, since …

The Boltzmann–Gibbs (BG) entropy and its associated statistical mechanics were
generalized, three decades ago, on the basis of the nonadditive entropy S q (q∈ R), which …

A new generalized uncertainty relation is constructed based on Li-Ostoja-Starzewski
fractional gradient operator of order 0< α≤ 1 introduced recently in literature which is …

In this study, the Schrödinger equation with position-dependent mass in fractal dimensions
is constructed from fractal anisotropy and product-like fractal measure introduced by Li and …

In this study, we introduce a new approach to construct the Schrödinger equation with
position-dependent mass characterized by an emerging particle's effective mass, in perfect …

In this study, we have constructed a generalized Schrödinger equation in fractal dimensions
characterized by an effective potential which is generated by a position-dependent mass …

A translation operator acting in a space with a diagonal metric is introduced to describe the
motion of a particle in a quantum system. We show that the momentum operator and, as a …

We show that a direct connection can be drawn, based on fundamental quantum principles,
between the Morse potential, extensively used as an empirical description for the atomic …

Dirac equation with spatially or position-dependent mass and an attractive Coulomb-like
field is constructed in Hausdorff dimension of order 0< α ≤ 1 0< α≤ 1. The lower and upper …

We consider canonically conjugated generalized space and linear momentum operators x^
q and p^ q in quantum mechanics, associated with a generalized translation operator which …