3 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 kBT >> ℏω and kBT << ℏω. Finally, analyze the case of average energy and compare your result with the quantum mechanical result.

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Q: Problem 2. Derive the transmission coefficient for the delta-function barrier: V(x) = a 8(x) (a >…

A: The required solution for the above problem is given below.