CLASSIC ORBIT OF QUANTUM ELECTRON AND THE ORIGIN OF BLACK HOLE ENTROPY

The question of one-dimensional oscillation driven by inverse square forces arises in two important scenarios in physics: the classical orbital interpretation of hydrogen atom electron wave functions and the Newtonian mechanical description of self-gravitating collapsing spheres. The popular viewpoint suggests that these two scenarios involve issues of “unrealistic orbital concepts” and “inapplicability of Newtonian mechanics” respectively, leading to a lack of in-depth exploration of this problem. This paper argues that the classical orbits of hydrogen atom electrons are not only real but also crucial in fundamentally understanding the area law featured entropy of black holes and their nontrivial internal structures. Depending on the classical interpretation of quantized wave functions, this internal structure can be understood as oscillatory modes of black hole matter contents over crossing the central point, or as oscillatory modes of those matters across the horizon surface itself with the inner space cut out completely.