Related papers: Analytic calculation of ground state splitting in …
We review an exact analytical resolution method for general one-dimensional (1D) quantal anharmonic oscillators: stationary Schr\"odinger equations with polynomial potentials. It is an exact form of WKB treatment involving spectral (usual)…
We study the effect of anharmonicity in quantum anharmonic oscillators, by computing the energy gap between the ground and the 1st excited state using the numerical bootstrap method. Based on perturbative formulae of limiting coupling…
Motivated by our earlier argument that the apparent large cosmological constant from quantum fluctuations is actually an artifact of not using a full quantum mechanical superposition to determine the ground state in which the universe lives…
Electron spin-qubits in silicon-germanium (SiGe) heterostructures are a major candidate for the realization of scalable quantum computers. A critical challenge in strained Si/SiGe quantum wells (QWs) is the existence of two nearly…
Using the effective mass model for an electron and the dielectric continuum model, analytical solutions of the self-consistent Schr\"odinger-Poisson system of equations are obtained. Quantum mechanical theory of electronic stationary…
Recently it was discovered that the ground state orbital angular momentum in two-dimensional chiral superfluids with pairing symmetry $(p_x+ip_y)^\nu$ depends on the winding number $\nu$ in a striking manner. The ground state value for the…
In a previous paper we solved a countably infinite family of one-dimensional Schr\"odinger equations by showing that they were supersymmetric partner potentials of the standard quantum harmonic oscillator. In this work we extend these…
The spin-1/2 Heisenberg model on the pyrochlore lattice is an iconic frustrated three-dimensional spin system with a rich phase diagram. Besides hosting several ordered phases, the model is debated to possess a spin-liquid ground state when…
For any central potential V in D dimensions, the angular Schroedinger equation remains the same and defines the so called hyperspherical harmonics. For non-central models, the situation is more complicated. We contemplate two examples in…
We investigate the electron states in double asymmetric $\rm{HgTe/Cd_{x}Hg_{1-x}Te}$ quantum wells grown along the $[001]$ direction. The subbands are computed by means of the envelope function approximation applied to the 8-band Kane…
The extended Bose-Hubbard model for a double-well potential with atom-pair tunneling is studied. Starting with a classical analysis we determine the existence of three different quantum phases: self-trapping, phase-locking and Josephson…
We study the spectral approximation of a second-order elliptic differential eigenvalue problem that arises from structural vibration problems using isogeometric analysis. In this paper, we generalize recent work in this direction. We…
A general procedure based on shift operators is formulated to deal with anharmonic potentials. It is possible to extract the ground state energy analytically using our method provided certain consistency relations are satisfied. Analytic…
In this paper, applying the Bethe ansatz method, we investigate the Schr\"odinger equation for the three quasi-exactly solvable double-well potentials, namely the generalized Manning potential, the Razavy bistable potential and the…
We determine the wave functions for arbitrarily polarized quantum Hall states by employing the doublet model which has been proposed recently to describe arbitrarily polarized quantum Hall states. Our findings recover the well known fully…
At one loop, we provide an explicit formula for the ground state of the one-soliton sector in the Sine-Gordon theory. The state is given in the basis of eigenstates of the field operator, or equivalently as a Schrodinger wave functional.…
A new model for the double well potential is presented in the paper. In the new potential, the exchanging rate could be easily calculated by the perturbation method in supersymmetric quantum mechanics. It gives good results whether the…
We report on results of numerical studies of the spin polarization of the half filled second Landau level, which corresponds to the fractional quantum Hall state at filling factor $\nu=5/2$. Our studies are performed using both exact…
The general formulation of a technically advantageous method to find the ground state solution of the Schrodinger equation in configuration space for systems with a number of particles A greater than 4 is presented. The wave function is…
We predict wide-band suppression of tunneling of spin-orbit-coupled atoms (or noninteracting Bose-Einstein condensate) in a double-well potential with periodically varying depths of the potential wells. The suppression of tunneling is…