Abstract
Abstract
In this work we solve the time-independent Schrödinger equation of a particle restricted to move on the surface of a circular cone of finite height. The energy eigenvalues, as well as the corresponding wave functions, are obtained analytically as a function of,
r
and
ϕ
,
the radial distance to the apex,
0
≤
r
≤
r
0
,
and the angular variable around the axis of the cone. We compute the Shannon entropy of this system in both configuration and momentum space as a function of
r
0
and
θ
0
,
the angular semi-aperture of the cone. In configuration space, the Shannon entropy decreases, signalling a more pronounced localization, as either
r
0
or
θ
0
diminish; in momentum space, an opposite behaviour happens, i.e., the Shannon entropy increases when either,
r
0
or
θ
0
,
decrease. We also compute the radial standard deviation; we find that the Shannon entropy better describes the localization-delocalization phenomena. The present results agree with those previously published for a particle confined to a circle of radius
r
0
,
which corresponds to
θ
0
=
π
/
2
in the present case.