Abstract
The vibrational frequency (VF), the ground state (GS) energy and the GS binding energy of the weak electron-phonon coupling polaron in a quantum well (QW) with asymmetrical Gaussian confinement potential are calculated. First we introduce the linear combination operator to express the momentum and coordinates in the Hamilton and then operate the system Hamilton using unitary transformation. The results indicate the relations of the quantities (the VF, the absolute value of GS energy and the GS binding energy) and the parameters (the QW barrier height and the range of Gaussian confinement potential in the growth direction of the QW).
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