Solve this problem in a quantum canonical ensemble. We have a one-dimensional oscillator of mass m and frequency . Find the correct probability density associated

Solve this problem in a quantum canonical ensemble. We have a one-dimensional oscillator of mass m and frequency ω. Find the correct probability density associated with position x and discuss its values at the following limits k_BT >> ℏω and k_BT << ℏω. Finally, analyze the case of average energy and compare your result with the quantum mechanical result.