Abstract: Considering the weak-coupling of electrons and optical phonons, the expression of phonon mean number of weak-coupling polaron in triangular quantum well is derived by combining linear combination operator with unitary transformation. The linear relationship between electron-phonon coupling coefficient and phonon mean number is found. Results show that the influence of electron-phonon coupling strength on the phonon mean number can’t be ignored. Taking the semiconductor weak-coupled material as an example, the definite proportionality between the two materials is discussed. The result has certain theoretical guiding significance in the practical research.

Key words: triangular quantum well, polaron, mean number of phonons, unitary transformation