  We theoretically analyze two setups of low energy single-photon counters
based on Josephson junctions (JJ). For this, we propose two simple and general
models, based on the macroscopic quantum tunneling formalism (MQT). The first
setup is similar to the photon counter based on the "cold electron bolometer"
(CEB), where the JJ replaces the CEB in the center of the superconducting
antenna. In the second setup, the JJ is capacitively coupled to the antenna. We
derive the Hamiltonians for the two setups and we write the Schr\"odinger
equations taking into account both, the antenna and the JJ. The quantum
particles of the MQT models are in two-dimensional potential landscapes, which
are parabolic along one direction and may have the form of a washboard
potential along another direction. Such a potential landscape has a series of
local minima, separated by saddle points. If the particle is prepared in the
initial state in the metastable "ground state" of a local minimum, then the
photon absorption causes it to jump into an excited state. If the excitation
energy is bigger than the potential barrier seen by the quantum particle (the
difference between the "ground state" and the saddle point), the photon is
detected.
  The models are simple and allow us to do mostly analytical calculations. We
show that the two setups are equivalent form the MQT point of view, since one
Hamiltonian can be transformed into the other by changes of variables. For
typical values of the JJ and antenna parameters, the setups may work as
counters of photons of wavelengths up to 1 cm, at least.
