Abstract
As soon as quantum mechanics was formulated by Schrodinger [1] as an eigenvalue problem, the problem of continuous spectrum arose as something new that did not exist (or was not recognized as such) in classical mathematical physics. The continuous spectrum is an essential ingredient of the Hamiltonian operator, and one is naturally led to the question of completeness for the (discrete and continuous) set of eigenfunctions. (It is strange that the same question for classical continuum mechanics was not considered until 1950 s, when Weyl [2] started to study the existence of solutions for the Dirichlet and Neumann problems for exterior domains.)
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Kato, T. (1977). Stationary Theory of Scattering. In: Thirring, W., Urban, P. (eds) The Schrödinger Equation. Acta Physica Austriaca, vol 17/1977. Springer, Vienna. https://doi.org/10.1007/978-3-7091-7673-3_5
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