Asymptotic expansion for the wave function in a one-dimensional model of inelastic interaction

We consider a two-body quantum system in dimension one composed by a test particle interacting with a harmonic oscillator placed at the position a > 0. At time zero the test particle is concentrated around the position R(0) with average velocity+/-v(0) while the oscillator is in its ground state. In a suitable scaling limit, corresponding for the test particle to a semiclassical regime with small energy exchange with the oscillator, we give a complete asymptotic expansion of the wave function of the system in both cases R(0) < a and R(0) > a. (C) 2011 American Institute of Physics. [doi:10.1063/1.3549587]