相关论文: Poeschl-Teller paradoxes

We find the existence of sub-Planck scale structures in the P{\"o}schl-Teller potential, which is an exactly solvable potential with both symmetric and asymmetric features. We analyze these structures in both cases by looking at the Wigner…

The double-layer potential plays an important role in solving boundary value problems for elliptic equations. All the fundamental solutions of the generalized bi-axially symmetric Helmholtz equation were known, and only for the first one…

One of the simplest pseudo-Hermitian models with real spectrum (viz., square-well on a real interval I of coordinates) is re-examined. A PT-symmetric complex deformation C of I is introduced and shown tractable via an innovated approach to…

Tunnelling from a chaotic potential well is explained in terms of a set of complex periodic orbits which contain information about the real dynamics inside the well as well as the complex dynamics under the confining barrier. These orbits…

Suitable complexification of the well known solvable oscillators in one dimension is shown to give the four exactly solvable models which combine the shape- and PT-invariance. In version v2 the result is extended of the s-wave…

The double-layer potential plays an important role in solving boundary value problems for elliptic equations, and in the study of which for a certain equation, the properties of the fundamental solutions of the given equation are used. All…

We show that and how the Coulomb potential can be regularized and solved exactly at the imaginary couplings. The new spectrum of energies is real and bounded as expected, but its explicit form proves totally different from the usual…

Multi-dimensional complex optical potentials with partial parity-time (PT) symmetry are proposed. The usual PT symmetry requires that the potential is invariant under complex conjugation and simultaneous reflection in all spatial…

Large families of Hamiltonians that are non-Hermitian in the conventional sense have been found to have all eigenvalues real, a fact attributed to an unbroken PT symmetry. The corresponding quantum theories possess an unconventional scalar…

Using the formalism of extended $N=4$ supersymmetric quantum mechanics we consider the procedure of the construction of multi--well potentials. We demostrate the form--invariance of Hamiltonians entering the supermultiplet, using the…

A long-standing problem in the foundations of quantum mechanics is to identify a physical principle that explains why algebraically maximal violations of Bell inequalities can generally not be achieved in Nature. One recently proposed…

We solve the infinite potential well problem using the methods of Heisenberg's matrix mechanics. In addition to being of educational value, the matrix mechanics allows us to deal with various unphysical issues caused by this potential in a…

The recently proposed PT-symmetric quantum mechanics works with complex potentials which possess, roughly speaking, a symmetric real part and an anti-symmetric imaginary part. We propose and describe a new exactly solvable model of this…

We consider a Parity-time (PT) invariant non-Hermitian quasi-exactly solvable (QES) potential which exhibits PT phase transition. We numerically study this potential in a complex plane classically to demonstrate different quantum effects.…

The supersymmetric solutions of PT-/non-PT-symmetric and non-Hermitian deformed Morse and P\"{o}schl-Teller potentials are obtained by solving the Schr\"{o}dinger equation. The Hamiltonian hierarchy method is used to get the real energy…

Dynamical systems exhibiting both PT and Supersymmetry are analyzed in a general scenario. It is found that, in an appropriate parameter domain, the ground state may or may not respect PT-symmetry. Interestingly, in the domain where…

We investigate complex PT-symmetric potentials, associated with quasi-exactly solvable non-hermitian models involving polynomials and a class of rational functions. We also look for special solutions of intertwining relations of SUSY…

The $\cal PT$-symmetric complexified Scarf II potential $V(x)= - V_1 \sech^{2}x + {\rm i} V_2 \sech x \tanh x$, $V_1>0$ , $V_{2}\neq 0$ is revisited to study the interplay among its coupling parameters. The existence of an isolated real and…

Symmetry-protected topological (SPT) phases are many-body quantum states that are topologically nontrivial as long as the relevant symmetries are unbroken. In this work we show that SPT phases are also well defined for average symmetries,…

Trigonometric invariants are defined for each Weyl group orbit on the root lattice. They are real and periodic on the coroot lattice. Their polynomial algebra is spanned by a basis which is calculated by means of an algorithm. The…