Bound state solutions of the hyper-radial Klein-Gordon equation under the Deng-Fan potential by WKB and SWKB method

The energy levels of the Klein-Gordon equation in hyper-radial space under the Deng-Fan potential energy function are studied by the SWKB and WKB approximation methods. We obtained the analytic solution of the energy spectra and the ground state wave function in closed form. Furthermore, we obtained the energy equation corresponding to the Schrodinger equation by invoking the non-relativistic limit. The variations of the non-relativistic N-dimensional energy spectra with the potential parameters and radial quantum number are investigated. The energy levels are degenerate for N= 2, N=4 and increase with the dimensionality number. The ground state wave function and its gradient are continuous at the boundary r=0,r=∞. Our results for the energy spectra are in excellent agreement with the ones obtained by other analytical methods where similar centrifugal approximations were applied. We show that the semi-classical methods notably the SWKB and WKB approximation still offer an effective and the simplest approach for solving the bound state problems in theoretical physics.

Ground state wave function overlap in superconductors and superfluids

In order to elucidate the quantum ground state structure of nonrelativistic condensates, we explicitly construct the ground state wave function for multiple species of bosons, describing either superconductivity or superfluidity. Since each field Ψj carries a phase θj and the Lagrangian is invariant under rotations θj → θj + αj for independent αj, one can investigate the corresponding wave function overlap between a pair of ground states $\langle G\vert {G}^{\prime }\rangle $ differing by these phases. We operate in the infinite volume limit and use a particular prescription to define these states by utilizing the position space kernel and regulating the UV modes. We show that this overlap vanishes for most pairs of rotations, including θj → θj + mj ϵ, where mj is the mass of each species, while it is unchanged under the transformation θj → θj + qj ϵ, where qj is the charge of each species. We explain that this is consistent with the distinction between a superfluid, in which there is a nontrivial conserved number, and the superconductor, in which the electric field and conserved charge is screened, while it is compatible with a nonzero order parameter in both cases. Moreover, we find that this bulk ground state wave function overlap directly reflects the Goldstone boson structure of the effective theory and provides a useful diagnostic of its physical phase.

A computationally-derived model for the solvatochromism of p-phenolates with high predictive power

We report that the positive, reverse or negative solvatochromism of p-phenolate-based dyes is highly correlated with the multireferential (MR) character of their ground-state wave function, with negative compounds presenting the highest degeneracy.