Incorporating the quantum of action h into classical physics

Investigate whether and how the quantum of action h can be incorporated into the framework of classical physics in a consistent manner, or otherwise ascertain the reasons such incorporation is not possible.

Background

Planck recounts that, after introducing the quantum of action h, he made repeated attempts over several years to reconcile this constant with classical physics. He explicitly states that these attempts failed, leaving open the question of whether a classical integration is possible at all.