For massive, non-interacting particles, the thermal de Broglie wavelength can be derived from the calculation of the partition function. Assuming a 1-dimensional box of length L, the partition function (using the energy states of the 1D particle in a box) is Z = ∑ ∑ n e − − E n / k B T = ∑ ∑ n e − − h 2 n 2 / 8 m L 2 k B T .