The " + 1 / 2 " can be thought of as linked to quantum fluctuations, or to zero-point motion of the observable x ^ ^ . At high enough temperatures, n B E ≈ ≈ ( β β ℏ ℏ ω ω ) − − 1 ≫ ≫ 1 , i.e. the quantum contribution is negligible, and we recover the classical version.