ABSTRACT
This chapter describes that the methods of Gross and Huybrechts, because these methods, with some shortcomings notwithstanding, have gained wider acceptance and are still being used by many researchers. One of the early methods which attempted to deal with the entire coupling range was by Hohler. In the Hohler method, one chooses a wave function by taking a linear combination of Pekar-type wave functions such that the trial wave function is an eigenfunction of the total momentum. The Lee-Low-Pines-Huybrechts (LLPH) method is a modified version of the Low-Lee-Pines (LLP) method that was developed by Huybrechts to address small-coupling region, as well. The LLP method was also modified by Gross to make it valid for the entire range of the coupling constant. This method can be easily seen to give the weak- and the strong-coupling limits. For the polaron radius, Landau-Pekar method however gives an infinite value.
