  We study the ladder operator on scalar fields, mapping a solution of the
Klein-Gordon equation onto another solution with a different mass, when the
operator is at most first order in derivatives. Imposing the commutation
relation between the d'Alembertian, we obtain the general condition for the
ladder operator, which contains a non-trivial case which was not discussed in
the previous work [V. Cardoso, T. Houri and M. Kimura, Phys.Rev.D 96, 024044
(2017), arXiv:1706.07339]. We also discuss the relation with supersymmetric
quantum mechanics.
