The Bound Polaron In Quantum Well In External Field

In the paper, the properties of bound polaron in external field in infinite quantum well are studied. We have derived the variational relation of the ground-state energy of the bound polaron in external field in quantum well with the Coulomb bound potential, external field and the well-width by using linear combination operator and unitary transformation methods. At the same time, we have also discussed the variational relation of the vibration frequency with the Coulomb bound potential, external field.It is shown by evaluating numerically that, when there is the magnetic field, the ground-state energy of the weak- and strong-coupling bound polaron is different because of different values of the Coulomb bound potential, magnetic field and the well-width. For the weak-coupling bound magnetopolaron, the ground-state energy will decrease with increasing the Coulomb bound potential, and it will increase with increasing magnetic field. When the magnetic field is strong, it will increase with increasing the well-width, when the magnetic field is weak, its absolute value will increase with increasing the well-width. The vibration frequency will increase with increasing the Coulomb bound potential and the electric field. For the strong-coupling bound magnetopolaron, the absolute value of the ground-state energy will decrease with increasing the vibration frequency and magnetic field; it will increase when the Coulomb bound potential and the well-width increase. When the Coulomb bound potential and the magnetic field take respectively a certain value, the ground-state energy will swiftly decrease with increasing the well-width.When there is the electric field, we have derived the dependence of the ground- state energy of the weak coupling bound polaron in quantum well on the Coulomb bound potential,the electric field,the well-width. The absolute value of the ground-state energy will increase with increasing the electric field and the Coulomb bound potential, and it will decrease with increasing the well width. At the same time, we have derived the square of the vibration frequency is proportional to the Coulomb bound potential. There is eighth the magnetic field or the electric field, the well width is small, the quantum size effect is significant.