Abstract: 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=1^∞ 1/n^2、∑n=1^∞ 1/n^4 , etc. are deduced. This is constructed by using the equivalence of the two different methods in calculating the normalization constant of wave function and the mean value of energy.

Key words: infinite square potential well, normalization constant, the mean value of energy, infinite series, summation formulas