  Confinement of atoms inside various cavities has been studied for nearly
eight decades. However, the Compton profile for such systems has not yet been
investigated. Here we construct the Compton profile (CP) for a H atom radially
confined inside a \emph{hard} spherical enclosure, as well as in \emph{free
condition}. Some exact analytical relations for the CP's of circular or
nodeless states of free atom is presented. By means of a scaling idea, this has
been further extended to the study of an H-like atom trapped inside an
impenetrable cavity. The accuracy of these constructed CP has been confirmed by
computing various momentum moments. Apart from that, several information
theoretical measures, like Shannon entropy ($S$) and Onicescu energy ($E$) have
been exploited to characterize these profiles. Exact closed form expressions
are derived for $S$ and $E$ using the ground state CP in free H-like atoms. A
detailed study reveals that, increase in confinement inhibits the rate of
dissipation of kinetic energy. At a fixed $\ell$, this rate diminishes with
rise in $n$. However, at a certain $n$, this rate accelerates with progress in
$\ell$. A similar analysis on the respective free counterpart displays an
exactly opposite trend as that in confined system. However, in both free and
confined environments, CP generally gets broadened with rise in $Z$.
Representative calculations are done numerically for low-lying states of the
confined systems, taking two forms of position-space wave functions: (a) exact
(b) highly accurate eigenfunctions through a generalized pseudospectral method.
In essence, CPs are reported for confined H atom (and isoelectronic series) and
investigated adopting an information-theoretic framework.
