  We study transport properties of an arbitrary two terminal Hermitian system
within a tight-binding approximation and derive the expression for the
transparency in the form, which enables one to determine exact energies of
perfect (unity) transmittance, zero transmittance (Fano resonance) and bound
state in the continuum (BIC). These energies correspond to the real roots of
two energy-dependent functions that are obtained from two non-Hermitian
Hamiltonians: the Feshbach's effective Hamiltonian and the auxiliary
Hamiltonian, which can be easily deduced from the effective one. BICs and
scattering states are deeply connected to each other. We show that
transformation of a scattering state into a BIC can be formally described as a
"phase transition" with divergent generalized response function. Design rules
for quantum conductors and waveguides are presented, which determine structures
exhibiting coalescence of both resonances and antiresonances resulting in the
formation of almost rectangular transparency and reflection windows. The
results can find applications in construction of molecular conductors, broad
band filters, quantum heat engines and waveguides with controllable BIC
formation.
