Taking the same trial wave function, the ground-state energy of Fröhlich polaron is investigated by variational method and coherent-state expansion (CSE) one, respectively. Within the accuracy to α 2 (the electron-phonon coupling constant), both methods can give the same analytic expressions of polaron groundstate energy as the function of electron-phonon coupling constant. We find that the CSE method can much simplify the calculation and shows more advantages in higher order approximations. PACS numbers: 71.38.-k, 63.20.Kr, 31.15.-p 1 Electron-phonon (e-p) interaction is an important elementary excitation in condensed matter physics. Although the Green Function method is quite mature to deal with such problems, it still can’t provide ideal results when the e-p interaction is relatively strong, such that, the variational method were often involved in consideration. Polaron problem is particular notable in ionic or semiconductor materials. Various approaches − had been applied to the calculation of polaron ground-state energy durin
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