Ring-shaped Non-spherical Oscillator Research Articles

Linear and nonlinear intersubband optical absorption coefficients and refractive index changes with the ring-shaped non-spherical oscillator potential

Linear and nonlinear intersubband optical absorption coefficients and refractive index changes with the ring-shaped non-spherical oscillator potential (RNOP) are theoretically investigated within the framework of the compact-density-matrix approach and iterative method. The energy levels and the wave functions of an electron in the RNOP are obtained by using the effective mass approximation. It is found that the optical absorption coefficients and refractive index changes are strongly affected not only by the dimensionless parameters γ and β, but also by the confinement frequency ω0.

Non-central potentials, exact solutions and Laplace transform approach

Exact bound state solutions and the corresponding wave functions of the Schrödinger equation for some non-central potentials including Makarov potential, modified-Kratzer plus a ring-shaped potential, double ring-shaped Kratzer potential, modified non-central potential and ring-shaped non-spherical oscillator potential are obtained by using the Laplace transform approach. The energy spectrums of the Hartmann potential, modified-Kratzer potential and ring-shaped oscillator potential are also briefly studied as special cases. It is seen that our analytical results for all these potentials are consistent with those obtained by other works. We also give some numerical results obtained for the modified non-central potential for different values of the related quantum numbers.

The position dependent band gap in Kane-type quantum dots

The energy spectrum of electrons in narrow band gap semiconductor nanocrystals which have position dependent band gap in an external non-uniform electric field which compensate the position dependence of the band edge of the valence band potential is studied theoretically taking into account the non-parabolicity of electrons in dispersion laws. The exact solutions of the Kane equations with strong spin–orbital interaction are determined via the band-gap changes as a function of position. The band edge gap potential is taken as the ring-shaped non-spherical oscillator potential

Bound states of Klein–Gordon equation and Dirac equation for ring-shaped non-spherical oscillator scalar and vector potentials

Solving the Klein–Gordon equation and Dirac equation with ring-shaped non-spherical oscillator gives the exact bound state wavefunction and energy equation and the relations between non-relativistic Schrodinger equation, Klein–Gordon equation and Dirac equation with equal scalar and vector potentials.

An algebraic approach to the ring-shaped non-spherical oscillator

The eigenfunctions and eigenvalues of the Schrödinger equation with a ring-shaped non-spherical oscillator are obtained. A realization of the ladder operators for the radial wave functions is studied. It is found that these operators satisfy the commutation relations of an SU(1,1) group. The closed analytical expressions for the matrix elements of different functions ρ and ρ d dρ with ρ= r 2 are evaluated.

Explicit expressions and recurrence formulas of the radial average values for a kind of nonharmonic oscillator model potentials

In this paper, two recurrence formulas are derived for the radial average values of a kind of non-harmonic oscillator model potentials; these non-harmonic oscillator model potentials are ring-shaped non-spherical oscillator, non-spherical oscillator, and ring-shaped oscillator. Explicit expressions for their radial average values are given.