&ldquo\;An observation of neutron
-antineutron oscillations (n-n ̅\;)\, which violate both B and B &mdas
h\; L conservation\, would constitute a scientific discovery of fundamenta
l importance to physics and cosmology. A stringent upper bound on its tran
sition rate would make an important contribution to our understanding of t
he baryon asymmetry of the universe by eliminating the post-sphaleron bary
ogenesis scenario in the light quark sector. We show that one can design a
n experiment using slow neutrons that in principle can reach the required
sensitivity of 10^{10 }s in the oscillation time\, an improvement
of 10^{4} in the oscillation probability relative to the existing
limit for free neutrons. This can be achieved by allowing both the neutron
and antineutron components of the developing superposition state to coher
ently reflect from mirrors. We present a quantitative analysis of this sce
nario and show that\, for sufficiently small transverse momenta of n/n
73\; and for certain choices of nuclei for the n/n ̅\; guide material\
, the relative phase shift of the n and n ̅\; components upon reflecti
on and the n ̅\; annihilation rate can be small. While the reflection
of n ̅\; from surface looks exotic and counterintuitive and seems to c
ontradict to the common sense\, in fact it is fully analogous to the refle
ction of n from surface. The later phenomenon is well known and used in ne
utron research from its first years. We illustrate it with two selected ex
ample of gravitational and whispering-gallery quantum states of neutrons.&
rdquo\;

\n[V.V. Nesvizhevsky\, A.Yu. Voronin\, Surprising Quantum Bounces\
, Imperial College Press\, London\, 2015] \;