Sakaguchi, H.; Malomed, B.A. Angular-Momentum Modes in a Bosonic Condensate Trapped in the Inverse-Square Potential. Symmetry2023, 15, 2060.
Sakaguchi, H.; Malomed, B.A. Angular-Momentum Modes in a Bosonic Condensate Trapped in the Inverse-Square Potential. Symmetry 2023, 15, 2060.
Sakaguchi, H.; Malomed, B.A. Angular-Momentum Modes in a Bosonic Condensate Trapped in the Inverse-Square Potential. Symmetry2023, 15, 2060.
Sakaguchi, H.; Malomed, B.A. Angular-Momentum Modes in a Bosonic Condensate Trapped in the Inverse-Square Potential. Symmetry 2023, 15, 2060.
Abstract
In the mean- field approximation, the well-known effect of the critical quantum collapse in a 3D
gas of particles pulled to the center by potential U(r) = -U_0/(2r^2) is suppressed by repulsive interparticle interactions, which create the otherwise non-existing s-wave ground state. Here, we address excited bound states carrying the angular momentum, with the orbital and magnetic quantum
numbers, l and m. They exist above a threshold value of the potential's strength, U_0 > l(l+1). The
sectoral, tesseral, and zonal modes, which correspond to m = l, 0 < m < l, and m = 0, respectively,
are found in an approximate analytical form for relatively small values of U_0 - l(l + 1). Explicit
results are produced for the p- and d-wave states, with l = 1 and 2, respectively. In the general form,
the bound states are obtained numerically, confirming the accuracy of the analytical approximation.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
