Quantum mechanics of the 1∕x2 potential | American Journal of Physics | AIP Publishing Skip
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The frequency of the breathing mode of a two-dimensional Fermi gas with zero-range
interactions in a harmonic confinement is fixed by the scale invariance of the Hamiltonian …

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 …

Particle motion at the microscale is an incessant tug-of-war between thermal fluctuations
and applied forces on one side and the strong resistance exerted by fluid viscosity on the …

In this Letter, we propose an experimental scheme for the observation of a quantum
anomaly—quantum-mechanical symmetry breaking—in a two-dimensional harmonically …

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 …

The similarity between classical and quantum physics is large enough to make an
investigation of quantization methods a worthwhile endeavour. As history has shown, Dirac's …

We use a toy model to illustrate how to build effective theories for singular potentials. We
consider a central attractive 1/r2 potential perturbed by a 1/r4 correction. The power …

The behavior of stochastic systems with interacting fast and slow degrees of freedom is
investigated both for discrete and continuous processes. Effective equations that govern the …

We study the radial Schrödinger equation for a particle of mass m in the field of a singular
attractive α/r 2 potential with 2 m α> 1/4. This potential is relevant to the fabrication of …