We show that a central 1/rn singular potential (with n>~ 2) is renormalized by a one-
parameter square-well counterterm; low-energy observables are made independent of the …

An anomaly is said to occur when a symmetry that is valid classically becomes broken as a
result of quantization. Although most manifestations of this phenomenon are in the context of …

The interaction of an electron with a polar molecule is shown to be the simplest realization of
a quantum anomaly in a physical system. The existence of a critical dipole moment for …

We present analytically the exact solutions of the Schrödinger equation in the N-dimensional
spaces for the pseudoharmonic oscillator potential by means of the ansatz method. The …

This article provides a focused review of recent findings which demonstrate, in some cases
quite counter-intuitively, the existence of bound states with a singularity of the density pattern …

A number of physical systems exhibit a particular form of asymptotic conformal invariance:
within a particular domain of distances, they are characterized by a long-range conformal …

Quantum collapse in three and two dimensions (3D and 2D) is induced by attractive
potential∼− r− 2. It was demonstrated that the mean-field (MF) cubic self-repulsion in the 3D …

We study the dynamics of rogue wave excitations and quasi-transitions in one-dimensional
quantum droplets, whose homogeneous-density flat top provides an applicable background …

We discuss a scenario in which the P c (4450)+ heavy pentaquark is a Σ c D¯*-Λ c (2595)
D¯ molecule. The Λ c 1 D¯→ Σ c D¯* transition is mediated by the exchange of a pion …

The quantum-mechanical collapse (alias fall onto the center of particles attracted by
potential-r-2) is a well-known issue in quantum theory. It is closely related to the quantum …