  The ladder operators in harmonic oscillator are a well-known strong tool for
various problems in physics. In the same sense, it is sometimes expected to
handle the problems of repulsive harmonic oscillator in a similar way to the
ladder operators in harmonic oscillators, though their analytic solutions are
well known. In this paper, we discuss a simple algebraic way to introduce the
ladder operators of the repulsive harmonic oscillators, which can reproduce
well-known analytic solutions. Applying this formalism, we discuss the charged
particles in a constant electric field in relation to the Schwinger effect; the
discussion is also made on a supersymmetric extension of this formalism.
