A fractional-dimensional space approach to the polaron effect in quantum wells

Polarons confined in rectangular and parabolic quantum wells are studied within the framework of the fractional-dimensional space approach. In this scheme, the real confined `polaron plus quantum well' system is mapped into an effective fractional-dimensional bulk in which the polaron behaves in an unconfined fashion, and the fractional dimension is essentially related to the degree of confinement of the actual system. Analytical expressions allowing a very simple estimation of the corresponding polaron corrections are found. The fractional-dimensional theoretical results are shown to be in reasonable agreement with previous more detailed calculations.