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It is shown that for the scalar analog of electrodynamics in one dimension, the quasinormal modes of a leaky cavity form a complete set inside the cavity, provided the cavity is defined by a discontinuity in the refractive index. This condition is sufficiently general to apply to a number of interesting examples. The quasinormal modes are also orthogonal under a modified definition of the inner product. The completeness and orthogonality hold even though the cavity is not a Hermitian system by itself. These properties allow the discrete quasinormal modes to be used as the basis for dynamics of the scalar wave in the cavity.
Leung et al. (Fri,) studied this question.