We study the quantum mechanical harmonic oscillator in two and three dimensions, with particular attention to the solutions as basis states for representing their respective symmetry groups — O(2), O(3), and O(2,1). Solving the Schrodinger equation by separating variables in polar coordinates, we obtain wavefunctions characterized by a principal quantum number, the group Casimir eigenvalue, and...

We identify all possible classes of solutions for two-component Bose-Einstein condensates (BECs) within the Thomas-Fermi (TF) approximation, and check these results against numerical simulations of the coupled Gross-Pitaevskii equations (GPEs). We find that they can be divided into two general categories. The first class contains solutions with a region of overlap between the components. The ot...

In this paper, the Hartree-Fock equations are proved to be the non relativistic limit of the Dirac-Fock equations as far as convergence of \stationary states" is concerned. This property is used to derive a meaningful deenition of \ground state" energy and \ground state" solutions for the Dirac-Fock model.

We consider the problem of reconstructing global quantum states from local data. Because the reconstruction problem has many solutions in general, we consider the reconstructed state of maximum global entropy consistent with the local data. We show that unique ground states of local Hamiltonians are exactly reconstructed as the maximal entropy state. More generally, we show that if the state in...

We study the performance of the D-Wave 2X quantum annealing machine on systems with well-controlled ground-state degeneracy. While obtaining the ground state of a spin-glass benchmark instance represents a difficult task, the gold standard for any optimization algorithm or machine is to sample all solutions that minimize the Hamiltonian with more or less equal probability. Our results show that...

We consider a class of fractional logarithmic Schrödinger equation in bounded domains. First, by means the constraint variational method, quantitative deformation lemma and some new inequalities, positive ground state solutions sign-changing are obtained. These inequalities derived from special properties equations critical for us to obtain our main results. Moreover, we show that energy any so...

The ground- and excited-state protonation of Coumarin 102 (C102), a fluorescent probe applied frequently in heterogeneous systems with an aqueous phase, has been studied in aqueous solutions by spectroscopic experiments and theoretical calculations. For the dissociation constant of the protonated form in the ground state, pKa = 1.61 was obtained from the absorption spectra; for the excited-stat...