相关论文: Spiked and PT-symmetrized decadic potentials suppo…

The pseudo-perturbation shifted-l expansion technique PSLET is shown applicable in the non-Hermitian PT-symmetric context. The construction of bound states for several PT-symmetric potentials is presented, with special attention paid to…

Bound states of the generalized spiked harmonic oscillator potential are calculated accurately by using the generalized pseudospectral method. Energy eigenvalues, various expectation values, radial densities are obtained through a…

Two-dimensional PT-symmetric quantum-mechanical systems with the complex cubic potential V_{12}=x^2+y^2+igxy^2 and the complex Henon-Heiles potential V_{HH}=x^2+y^2+ig(xy^2-x^3/3) are investigated. Using numerical and perturbative methods,…

The upside-down $-x^4$, $-x^6$, and $-x^8$ potentials with appropriate PT-symmetric boundary conditions have real, positive, and discrete quantum-mechanical spectra. This paper proposes a straightforward macroscopic quantum-mechanical…

The spectrum of complex PT-symmetric potential, $V(x)=igx$, is known to be null. We enclose this potential in a hard-box: $V(|x| \ge 1) =\infty $ and in a soft-box: $V(|x|\ge 1)=0$. In the former case, we find real discrete spectrum and the…

This note examines Gross-Pitaevskii equations with PT-symmetric potentials of the Wadati type: $V=-W^2+iW_x$. We formulate a recipe for the construction of Wadati potentials supporting exact localised solutions. The general procedure is…

We study the spectrum in such a PT-symmetric square well of a diameter L where the "strength of the non-Hermiticity" is controlled by the two parameters, viz., by an imaginary coupling ig and by the distance d of its onset from the origin.…

We consider the question of the number of exactly solvable complex but PT-invariant reflectionless potentials with $N$ bound states. By carefully considering the $X_m$ rationally extended reflectionless potentials, we argue that the total…

In this paper we study the number of the boundary single peak solutions of the problem {align*} {cases} -\varepsilon^2 \Delta u + u = u^p, &\text{in}\Omega u > 0, &\text{in}\Omega \frac{\partial u}{\partial \nu} = 0,& \text{on}\partial…

We study existence and multiplicity of semi-classical states for the nonlinear Choquard equation: $$ -\varepsilon^2\Delta v+V(x)v = \frac{1}{\varepsilon^\alpha}(I_\alpha*F(v))f(v) \quad \hbox{in}\ \mathbb{R}^N, $$ where $N\geq 3$,…

We present explicit constructions of centrally symmetric polytopes with many faces: first, we construct a d-dimensional centrally symmetric polytope P with about (1.316)^d vertices such that every pair of non-antipodal vertices of P spans…

We study the bound states of a Kronig Penney potential for a nonlinear one-dimensional Schroedinger equation. This potential consists of a large, but not necessarily infinite, number of equidistant delta-function wells. We show that the…

The D -dimensional quasi - exact solutions for the singular even - power anharmonic potential $V(q)=aq^2+bq^{-4}+cq^{-6}$ are reported. We show that whilst Dong and Ma's [5] quasi - exact ground - state solution (in D=2) is beyond doubt,…

We obtain the band edge eigenstates and the mid-band states for the complex, PT-invariant generalized associated Lam\'e potentials $V^{PT}(x)=-a(a+1)m \sn^2(y,m)-b(b+1)m {\sn^2 (y+K(m),m)} -f(f+1)m {\sn^2 (y+K(m)+iK'(m),m)}-g(g+1)m {\sn^2…

The family of complex PT-symmetric sextic potentials is studied to show that for various cases the system is essentially quasi-solvable and possesses real, discrete energy eigenvalues. For a particular choice of parameters, we find that…

We solve the Duffin-Kemmer-P\'{e}tiau equation in the presence of a spatially one-dimensional symmetric potential well. We compute the scattering state solutions and we derive conditions for transmission resonances. The bound solutions are…

We construct exact localised solutions of the PT-symmetric Gross-Pitaevskii equation with an attractive cubic nonlinearity. The trapping potential has the form of two $\delta$-function wells, where one well loses particles while the other…

We study a three-parameter family of PT-symmetric Hamiltonians, related via the ODE/IM correspondence to the Perk-Schultz models. We show that real eigenvalues merge and become complex at quadratic and cubic exceptional points, and explore…

We show that it needs a more delicate potential to confine particles inside a well. The original model containing a vague notation of infinity in the potential energy is ambiguous. Using the Heaviside step function and the Dirac…

One-dimensional potentials defined by $V^{(S)}(x) =S(S+1) \hbar^2 \pi^2 /[2ma^2\sin^2(\pi x/a)]$ (for integer $S$) arise in the repeated supersymmetrization of the infinite square well, here defined over the region $(0,a)$. We review the…