which is the product of the form factor and the Fourier transform of either the sum of the barriers or the difference of the barriers, depending on the parities of the initial and final states.

Two conclusions can be readily drawn from Eq. (\[W\_equivalent\_particles\]): First, considering tunneling within the time-independent picture, Amirkhanov and Zakhariev [@Amirkhanov1966] have discovered the violation of the barrier penetration symmetry for complex particles, i.e., the penetration of composite particles through asymmetric barriers in opposite directions may differ. \[Note that the rates of tunneling of an elementary (structureless) particle are exactly the same in both the directions within the time-independent approach.\] The situations when the system approaches the barrier from the left and from the right differ only by inversion of the sign of the momentum of the center of mass. The only part of the wave function (\[Psi\_at\_plus\_infty\]) that maintains the dependence on the sign of the momentum is the matrix element (\[Simplified\_W\_general\]). Thus, the discussed phenomenon of tunneling asymmetry is manifested in our consideration as a physical consequence of the property $$\begin{aligned}
\label{SymmetryW}
W_{n n'}(k'-k) = W_{n n'}(k-k') \Longleftrightarrow V_1(q) = V_2(-q).\end{aligned}$$ Equation (\[SymmetryW\]) is not only an alternative and perhaps faster way of achieving 