The mean number of phonons, the ground state energy of the weak-coupling magnetopolaron and the ratio(absolute value) of the electron spin energy to the ground state energy in an infinite quantum well were derived.

In this paper,A new cyclic model of quantum Carnot heat engine whose working substance consists of non-interacting extreme relativistic particles confined to an infinite potential well,is set up.

<Abstrcat> In this paper, the formation of the lowest subband states in symmetric coupled quantum-well is discussed with the use of an infinite-potential-well model, and the evolvement rules of the lowest subband states in the presence of an electric field along the direction of the well are analyzed with the use of two-energy-level system at length.

new method of calculating summation of series is constructed by using a set of suitable wave functions in an infinite square potential well of one dimension.

On the basis of the analytical solution in an infinite square potential well of one dimension, this paper deduces 24 summation formulas of infinite series, such as n=11n~(2),(n=11n~(4), etc.

The operator theory method lead to the uncertainty relation of one dimensional infinite well;

Using the nonlinear Lee algebra, we give a class of new coherent states for symmetrical one-dimensional infinitely deep square well potential, and we find there is a non-classical effect in these coherent states.