  It is generally believed that classical regime emerges as a limiting case of
quantum theory. Exploring such quantum-classical correspondences in a more
transparent manner is central to the deeper understanding of foundational
aspects and has attracted a great deal of attention - starting from the early
days of quantum theory. While it is often highlighted that quantum to classical
transition occurs in the limit hbar tending to zero, several objections have
been raised about its suitability in some physical contexts. Ehrenfest's
theorem is another widely discussed classical limit - however, its inadequacy
has also been pointed out in specific examples. It has been proposed that since
a quantum mechanical wave function inherits an intrinsic statistical behavior,
its classical limit must correspond to a classical ensemble - not an individual
particle. This opens up the question "how would uncertainty relations of
canonical observables compare themselves in quantum and classical realms?" In
this paper we explore parallels between uncertainty relations in stationary
states of quantum systems and that in the corresponding classical ensemble. We
confine ourselves to one dimensional conservative systems and show, with the
help of suitably defined dimensionless physical quantities, that first and
second moments of the canonical observables match with each other in classical
and quantum descriptions - resulting in an identical structure for uncertainty
relations in both the realms.
