Analytical solution of the Duffin - Kemmer - Petiau equation for the sum of the Manning - Rosen and the Yukawa class potential

This paper presents an analytical bound-state solution to the Duffin - Kemmer - Petiau equation for the new putative combined Manning - Rosen and Yukawa class potentials. Using the developed scheme to approximate and overcome the difficulties arising in the centrifugal part of the potential, the bound-state solution of the modified Duffin - Kemmer - Petiau equation is found. Analytical expressions of energy eigenvalue and the corresponding radial wave functions are obtained for an arbitrary value of the orbital quantum number l . Also, eigenfunctions are expressed in terms of hypergeometric functions. It is shown that energy levels and eigenfunctions are quite sensitive to the choice of radial and orbital quantum numbers.

Positive bound state solutions for the nonlinear Schrödinger–Poisson systems with potentials

In this paper, we study the following Schrödinger–Poisson system in $\mathbb{R} ^{3}$R3$$ \textstyle\begin{cases} (-\Delta )^{\sigma }u+A(y)u+B(y)\phi (y)u=b(y) \vert u \vert ^{p-1}u, & y \in \mathbb{R} ^{3}, \\ (-\Delta )^{\sigma }\phi =B(y)u^{2}, & y\in \mathbb{R} ^{3}, \end{cases} $${(−Δ)σu+A(y)u+B(y)ϕ(y)u=b(y)|u|p−1u,y∈R3,(−Δ)σϕ=B(y)u2,y∈R3, with $\frac{3}{4}<\sigma <1$34<σ<1, $p\in (3,\frac{3+2\sigma }{3-2 \sigma })$p∈(3,3+2σ3−2σ). Then, under some suitable assumptions on the coefficients not requiring any symmetry property, we prove the existence of a bound state solution of the above problem.

Monopole–antimonopole: interaction, scattering and creation

The interaction of a magnetic monopole–antimonopole pair depends on their separation as well as on a second ‘twist’ degree of freedom. This novel interaction leads to a non-trivial bound state solution known as a sphaleron and to scattering in which the monopole–antimonopoles bounce off each other and do not annihilate. The twist degree of freedom also plays a role in numerical experiments in which gauge waves collide and create monopole–antimonopole pairs. Similar gauge wavepacket scatterings in the Abelian–Higgs model lead to the production of string loops that may be relevant to superconductors. Ongoing numerical experiments to study the production of electroweak sphalerons that result in changes in the Chern–Simons number, and hence baryon number, are also described but have not yet met with success. This article is part of a discussion meeting issue ‘Topological avatars of new physics’.