36 research outputs found
The Definability of Fields
We look for a deep connection between mathematics and physics. Our approach
is to propose a set theory T which leads to a concise mathematical description
of physical fields and to a finite unit of action. The concept of
"definability" of fields is then introduced. Definabilty of fields in T is
necessary and sufficient for quantization and sufficient to avoid physical
antinomies.Comment: 10 Pages. Typo corrected. This paper has been submitted to Chaos,
Solitons and Fractal
A general scheme for the effective-mass Schrodinger equation and the generation of the associated potentials
A systematic procedure to study one-dimensional Schr\"odinger equation with a
position-dependent effective mass (PDEM) in the kinetic energy operator is
explored. The conventional free-particle problem reveals a new and interesting
situation in that, in the presence of a mass background, formation of bound
states is signalled. We also discuss coordinate-transformed, constant-mass
Schr\"odinger equation, its matching with the PDEM form and the consequent
decoupling of the ambiguity parameters. This provides a unified approach to
many exact results known in the literature, as well as to a lot of new ones.Comment: 16 pages + 1 figure; minor changes + new "free-particle" problem;
version published in Mod. Phys. Lett.
PT-symmetric Solutions of Schrodinger Equation with position-dependent mass via Point Canonical Transformation
PT-symmetric solutions of Schrodinger equation are obtained for the Scarf and
generalized harmonic oscillator potentials with the position-dependent mass. A
general point canonical transformation is applied by using a free parameter.
Three different forms of mass distributions are used. A set of the energy
eigenvalues of the bound states and corresponding wave functions for target
potentials are obtained as a function of the free parameter.Comment: 13 page