  Theoretically, in (1+1) dimensions, one can have Klein-Fock-Gordon-Majorana
(KFGM) particles. More precisely, these are one-dimensional (1D)
Klein-Fock-Gordon (KFG) and Majorana particles at the same time. In principle,
the wave equations considered to describe such first-quantized particles are
the standard 1D KFG equation and/or the 1D Feshbach-Villars (FV) equation, each
with a real Lorentz scalar potential and some kind of Majorana condition. The
aim of this paper is to analyze the latter assumption fully and systematically;
additionally, we introduce specific equations and boundary conditions to
characterize these particles when they lie within an interval (or on a line
with a tiny hole at a point). In fact, we write first-order equations in the
time derivative that do not have a Hamiltonian form. We may refer to these
equations as first-order 1D Majorana equations for 1D KFGM particles. Moreover,
each of them leads to a second-order equation in time that becomes the standard
1D KFG equation when the scalar potential is independent of time. Additionally,
we examine the nonrelativistic limit of one of the first-order 1D Majorana
equations.
