QHO Z = 1/(2 sinh(βℏω/2)) ≡ exp/geom form; βℏω=log 4 ⇒ Z = 2/3

Sympy-exact symbolic witness of the QHO partition-function identity and a canonical intermediate-temperature evaluation. Setup: Z_sinh = 1 / (2 sinh(β ℏω/2)); Z_exp = e^{−βℏω/2} / (1 − e^{−βℏω}); apply .rewrite(exp) to Z_sinh and…