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Black hole thermodynamical entropy
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 …
gravitation, lie outside the validity of the Boltzmann–Gibbs (BG) theory. Consistently, since …
Economics and Finance: q-Statistical Stylized Features Galore
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 …
generalized, three decades ago, on the basis of the nonadditive entropy S q (q∈ R), which …
A new approach to the Schrodinger equation with position-dependent mass and its implications in quantum dots and semiconductors
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 …
position-dependent mass characterized by an emerging particle's effective mass, in perfect …
Position-dependent mass fractal Schrodinger equation from fractal anisotropy and product-like fractal measure and its implications in quantum dots and nanocrystals
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 …
is constructed from fractal anisotropy and product-like fractal measure introduced by Li and …
On a new fractional uncertainty relation and its implications in quantum mechanics and molecular physics
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 …
fractional gradient operator of order 0< α≤ 1 introduced recently in literature which is …
Quantum dots and cuboid quantum wells in fractal dimensions with position-dependent masses
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 …
characterized by an effective potential which is generated by a position-dependent mass …
Dirac equation with position-dependent mass and Coulomb-like field in Hausdorff dimension
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 …
field is constructed in Hausdorff dimension of order 0< α ≤ 1 0< α≤ 1. The lower and upper …
[HTML][HTML] Extended uncertainty from first principles
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 …
motion of a particle in a quantum system. We show that the momentum operator and, as a …
Morse potential derived from first principles
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 …
between the Morse potential, extensively used as an empirical description for the atomic …
Quantum mechanics with spatial non-local effects and position-dependent mass
A new higher order Schrödinger equation characterized by a position-dependent mass is
introduced based on long-range spatial kernel effects and von Roos arguments. The …
introduced based on long-range spatial kernel effects and von Roos arguments. The …