Abstract
AbstractIn this work, we focus on some connections that exist between the Riccati and Ermakov–Milne–Pinney equations, particularly those which are established via the Schrödinger equation. Some formulas that express the general solution of the Riccati and Schrödinger equations in terms of a particular solution of the Riccati equation are obtained. It is shown that the difference between the general and particular solutions of the normal Riccati equation satisfies the Ermakov–Milne–Pinney equation with λ = −1/4. The formulas derived in this work are discussed in view of their quantum chemical applications, especially related to the WKB approach that is applied to describe the semiclassical behavior of molecules. This discussion is illustrated by a simple model of quantum harmonic oscillator. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009
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