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Asymptotic equations for the harmonic-oscillator representation

In the harmonic oscillator representation, the Schrödinger equation has a form of a set of infinite number of algebraical equations which are labeled by the radial quantum number n. It is shown that at n ≫ 1 these equations are significantly simplified and become an algebraical analogue of the original differential Schrödinger equation. This result is generalized to the case of multi-channel systems being studied in the framework of the resonating group method.