**The Israel Physical Society**

Home
About/Contact
Newsletters
Events/Seminars
2020 IPS Conference
Study Materials
Corporate Members

Home
About/Contact
Newsletters
Events/Seminars
2020 IPS Conference
Study Materials
Corporate Members

- IPS Conference 2020

We consider the problem of a quantum particle in a spherical potential well confined by a cone. By varying the apex angle 2*θ*_{0 }of the cone we modify the confinement of the particle from being inside a needle-like space via hemisphere and to an almost complete sphere with an excluded needle-like volume. In an infinite spherical well the energy spectrum is discrete and is determined by the zeros of the spherical Bessel functions, whose order is determined by *θ*_{0}. We numerically demonstrated, for several values of *θ*_{0}, that the total number of eigenstates up to energy *E* is correctly given by Weyl’s formula [1].

For the spherical well of a finite depth *-U*, there is a discrete energy spectrum of bound states with eigenenergies *E*<0 and a continuous spectrum of states with *E*>0, as long as the well is deep enough. For each *θ*_{0} there is a critical depth *U _{c}* at which the last bound state disappears. The bound states are localized inside the well such that outside the well the wavefunctions decay over a length scale (localization length) ξ. Close to the critical depth

[1] V. Ivrii, Bull. Math. Sci. **6 **(2016).

Copyright (c) 2008 Israel Physical Society