  In the context of General Relativity (GR), violation of the null energy
condition (NEC) is necessary for existence of static spherically symmetric
wormhole solutions. Also, it is a well-known fact that the energy conditions
are violated by certain quantum fields, such as the Casimir effect. The
magnitude and sign of the Casimir energy depend on Dirichlet or Neumann
boundary conditions and geometrical configuration of the objects involved in a
Casimir setup. The Casimir energy may act as an ideal candidate for the matter
that supports the wormhole geometry. In the present work, we firstly find
traversable wormhole solutions supported by a general form for the Casimir
energy density assuming a constant redshift function. As well, in this
framework, assuming that the radial pressure and energy density obey a linear
equation of state, we derive for the first time Casimir traversable wormhole
solutions admitting suitable shape function. Then, we consider three geometric
configurations of the Casimir effect such as (i) two parallel plates, (ii) two
parallel cylindrical shells, and (iii) two spheres. We study wormhole solutions
for each case and their property in detail. We also check the weak and strong
energy conditions in the spacetime for the obtained wormhole solutions. The
stability of the Casimir traversable wormhole solutions are investigated using
the Tolman-Oppenheimer-Volkoff (TOV) equation. Finally, we study trajectory of
null as well as timelike particles in the wormhole spacetime.
