Abstract: The dimension for infinite potential and finite potential quantum well is discussed. The dimension of infinite potential well monotonically decreases from 3 to 2 with the decrease of well width. In finite potential well, the dimension of quantum well tends to 3 when the well width is larger or goes to zero. As the well width decreases, the dimensions of the quantum well decreases firstly and then increase, and have their minima.

Key words: fractional dimension, quantum well