101 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
Supersymmetry Across Nanoscale Heterojunction
We argue that supersymmetric transformation could be applied across the
heterojunction formed by joining of two mixed semiconductors. A general
framework is described by specifying the structure of ladder operators at the
junction for making quantitative estimation of physical quantities. For a
particular heterojunction device, we show that an exponential grading inside a
nanoscale doped layer is amenable to exact analytical treatment for a class of
potentials distorted by the junctions through the solutions of transformed
Morse-Type potentials.Comment: 7 pages, 2 figure
A study of the bound states for square potential wells with position-dependent mass
A square potential well with position-dependent mass is studied for bound
states. Applying appropriate matching conditions, a transcendental equation is
derived for the energy eigenvalues. Numerical results are presented graphically
and the variation of the energy of the bound states are calculated as a
function of the well-width and mass.Comment: To appear in Phys. Lett. A (Present e-mail of A.G:
[email protected]
Exact solvability of potentials with spatially dependent effective masses
We discuss the relationship between exact solvability of the Schroedinger
equation, due to a spatially dependent mass, and the ordering ambiguity. Some
examples show that, even in this case, one can find exact solutions.
Furthermore, it is demonstrated that operators with linear dependence on the
momentum are nonambiguous.Comment: 12 page
Exceptional orthogonal polynomials and exactly solvable potentials in position dependent mass Schroedinger Hamiltonians
Some exactly solvable potentials in the position dependent mass background
are generated whose bound states are given in terms of Laguerre- or Jacobi-type
exceptional orthogonal polynomials. These potentials are shown to be
shape invariant and isospectral to the potentials whose bound state solutions
involve classical Laguerre or Jacobi polynomials.Comment: To appear in Physics Letters
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.
Development of an eight-band theory for quantum-dot heterostructures
We derive a nonsymmetrized 8-band effective-mass Hamiltonian for quantum-dot
heterostructures (QDHs) in Burt's envelope-function representation. The 8x8
radial Hamiltonian and the boundary conditions for the Schroedinger equation
are obtained for spherical QDHs. Boundary conditions for symmetrized and
nonsymmetrized radial Hamiltonians are compared with each other and with
connection rules that are commonly used to match the wave functions found from
the bulk kp Hamiltonians of two adjacent materials. Electron and hole energy
spectra in three spherical QDHs: HgS/CdS, InAs/GaAs, and GaAs/AlAs are
calculated as a function of the quantum dot radius within the approximate
symmetrized and exact nonsymmetrized 8x8 models. The parameters of dissymmetry
are shown to influence the energy levels and the wave functions of an electron
and a hole and, consequently, the energies of both intraband and interband
transitions.Comment: 36 pages, 10 figures, E-mail addresses: [email protected],
[email protected]
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