Adiabatic description of impenetrable particles in an infinitely deep potential well

In the framework of adiabatic approximation the energy spectrum and wave functions of two impenetrable particles in an infinitely deep potential well are considered for two cases of approximation of the effective confining potential of the ??slow?? subsystem. In case of the quadraticterm approximation the obtained energy spectrum is equidistant. The probability distribution in the range of ??fast?? particle has a symmetric shape while that in the range of the ??slow?? particle is asymmetric and the peak of localization of the system in its ground state is shifted towards the ??fast?? particle. In the first excited state the center of the probability distribution of the ??slow?? particle is shifted towards the impenetrable wall.