Numerical Computation of Circumferential Waves in Cylindrical Curved Waveguides

We present a complex field general variational statement to study the waves propagating in the circumferential directions of cylindrical curved waveguides. A semi-analytical technique that has been applied on straight waveguides in the literature is reformulated to adapt to the circumferential directions and used for constructing the trial wavefunction in complex field. The method requires the waveguide to be analyzed to be geometrically and physically uniform along its circumferential axis; however, its circumferential cross-section can be arbitrarily complex. The formulation is verified using various examples, which were examined previously by other numerical or analytical solutions. Different cases were studied and comparisons with those published are also performed show the utility and advantages of present method.

First-excited-state energy of hydrogenic impurity bound polaron in an anisotropic quantum dot in an electric field

The first-excited-state (ES) binding energy of hydrogenic impurity bound polaron in an anisotropic quantum dot (QD) is obtained by constructing a variational wavefunction under the action of a uniform external electric field. As for a comparison, the ground-state (GS) binding energy of the system is also included. We apply numerical calculations to KBr QD with stronger electron–phonon (E–P) interaction in which the new variational wavefunction is adopted. We analyzed specifically the effects of electric field and the effects of both the position of the impurity and confinement lengths in the xy-plane and the [Formula: see text] direction on the ground and the first-ES binding energies (BEs). The results show that the selected trial wavefunction in the ES is appropriate and effective for the current research system.

Nonlinear absorption coefficient and refractive index changes of two-dimensional two-electron quantum dot in rigid confinement

The Hamiltonian and wavefunctions describing two-dimensional (2D) two-electron ZnO quantum dot in rigid confinement are developed. Then the Schrödinger equation is solved analytically and numerically for determining the ground and excited state energies. The ground state energy of 2D two-electron ZnO quantum dot (QD) in rigid confinement is studied using perturbation and variational methods. The obtained result show that our trial wavefunction is good enough to describe the 2D two-electron QD in rigid confinement. The wavefunction describing the ground state is the combination of symmetric spatial wavefunction and antisymmetric spin wavefunction which is a para-state. The ground state energy eigenvalue obtained by variational technique is a little above that of a perturbation technique. Based on this; the trial wavefunction for the excited state is developed. The excited state energy of 2D two-electron ZnO QD in rigid confinement is studied computationally using variational method. The wavefunction describing the excited state is the combination of symmetric spatial wavefunction with antisymmetric spin wavefunction (para-state) or vice versa (ortho-state). The para and ortho-state energies of the first excited state are calculated and their difference is twice of the exchange energy. Based on the obtained energy eigenvalues of the ground and the first excited state at the value of the coupling constant [Formula: see text] [Formula: see text] 1, the third-order nonlinear absorption coefficient and refractive index changes are investigated. The optical transition is only considered between the two lowest para states.

Singlet–triplet gaps in diradicals obtained with diffusion quantum Monte Carlo using a Slater–Jastrow trial wavefunction with a minimum number of determinants

Reliable singlet–triplet gaps of diradicals are achieved with FN-DMC using the simplest ansatz for the trial wavefunction.

Diffusion and Reptation Quantum Monte Carlo Study of the NaK Molecule

<p>Diffusion Monte Carlo (DMC) and Reptation Monte Carlo (RMC) methods, have been applied to study some properties of the NaK molecule. Hartree-Fock (HF), Density Functional (DFT) and single and double configuration interaction (SDCI) wavefunctions with a valence quadruple zeta atomic natural orbital (VQZ/ANO) basis set were used as trial wavefunctions. Values for the potential energy curve, dissociation energy and dipole moment were calculated for all methods and compared with experimental results and previous theoretical derivations. Quantum Monte Carlo (QMC) calculations were shown to be useful methods to recover correlation in NaK, essential to obtain a reasonable description of the molecule. The equilibrium distance—interpolated from the potential energy curves—yield a value of 3.5 Å, in agreement with the experimental value. The dissociation energy, however, is not as good. In this case, a conventional CCSD(T) calculation with an extended aug-pc-4 basis set gives a much better agreement to experiment. On the contrary, the CCSD(T), other MO and DFT methods are not able to reproduce correctly the large dipole moment of this molecule. Even DMC methods with a simple HF trial wavefunction are able to give a better agreement to experiment. RMC methods are even better, and the value obtained with a B3LYP trial wavefunction is very close to the experimental one.</p>

Diffusion and Reptation Quantum Monte Carlo Study of the NaK Molecule

<p>Diffusion Monte Carlo (DMC) and Reptation Monte Carlo (RMC) methods, have been applied to study some properties of the NaK molecule. Hartree-Fock (HF), Density Functional (DFT) and single and double configuration interaction (SDCI) wavefunctions with a valence quadruple zeta atomic natural orbital (VQZ/ANO) basis set were used as trial wavefunctions. Values for the potential energy curve, dissociation energy and dipole moment were calculated for all methods and compared with experimental results and previous theoretical derivations. Quantum Monte Carlo (QMC) calculations were shown to be useful methods to recover correlation in NaK, essential to obtain a reasonable description of the molecule. The equilibrium distance—interpolated from the potential energy curves—yield a value of 3.5 Å, in agreement with the experimental value. The dissociation energy, however, is not as good. In this case, a conventional CCSD(T) calculation with an extended aug-pc-4 basis set gives a much better agreement to experiment. On the contrary, the CCSD(T), other MO and DFT methods are not able to reproduce correctly the large dipole moment of this molecule. Even DMC methods with a simple HF trial wavefunction are able to give a better agreement to experiment. RMC methods are even better, and the value obtained with a B3LYP trial wavefunction is very close to the experimental one.</p>

Diffusion and Reptation Quantum Monte Carlo Study of the NaK Molecule

<p>Diffusion Monte Carlo (DMC) and Reptation Monte Carlo (RMC) methods, have been applied to study some properties of the NaK molecule. Hartree-Fock (HF), Density Functional (DFT) and single and double configuration interaction (SDCI) wavefunctions with a valence quadruple zeta atomic natural orbital (VQZ/ANO) basis set were used as trial wavefunctions. Values for the potential energy curve, dissociation energy and dipole moment were calculated for all methods and compared with experimental results and previous theoretical derivations. Quantum Monte Carlo (QMC) calculations were shown to be useful methods to recover correlation in NaK, essential to obtain a reasonable description of the molecule. The equilibrium distance—interpolated from the potential energy curves—yield a value of 3.5 Å, in agreement with the experimental value. The dissociation energy, however, is not as good. In this case, a conventional CCSD(T) calculation with an extended aug-pc-4 basis set gives a much better agreement to experiment. On the contrary, the CCSD(T), other MO and DFT methods are not able to reproduce correctly the large dipole moment of this molecule. Even DMC methods with a simple HF trial wavefunction are able to give a better agreement to experiment. RMC methods are even better, and the value obtained with a B3LYP trial wavefunction is very close to the experimental one.</p>

Oscillator strength and quantum-confined Stark effect of excitons in a thin PbS quantum disk

In this paper, we report a study of the effect of a lateral electric field on a quantum-confined exciton in a thin PbS quantum disk. Our approach was performed in the framework of the effective mass theory and adiabatic approximation. The ground state energy and the stark shift were determined by using a variational method with an adequate trial wavefunction, by investigating a 2D oscillator strength under simultaneous consideration of the geometrical confinement and the electric field strength. Our results showed a strong dependence of the exciton binding and the Stark shift on the disk dimensions in both axial and longitudinal directions. On the other hand, our results also showed that the Stark shift’s dependence on the electric field is not purely quadratic but the linear contribution is also important and cannot be neglected, especially when the confinement gets weaker.

Intense laser field and conduction band-edge nonparabolicity effects on hydrogenic impurity states of InGaN QW

In this paper, hydrogenic impurity ground-state binding energy in unstrained wurtzite (In, Ga)N symmetric quantum well is investigated. The heterostructure is considered under the action of an intense laser field (ILF) incorporating an additional internal probe as well as the conduction band-edge nonparabolicity effect (CBENP). The variational approach is used within the framework of single band effective-mass approximation with two-parametric 1S-hydrogenic trial wavefunction. The competition effect between internal and external perturbations is also shown. Our results reveal that the binding energy is the largest for the well width around the effective Bohr radius and is strongly influenced by both parameters. Moreover, the principle effect of ILF (CBENP) is to reduce (enhance) the binding energy. It is found that the lift of the conduction band-edge can be easily eliminated by adjusting the ILF-parameter.