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Quantum mechanics is considered to arise from an underlying classicalstructure (``hidden variable theory'', ``sub-quantum mechanics''), wherequantum fluctuations follow from a physical noise mechanism. The stability ofthe hydrogen ground state can then arise from a balance between Lorentz dampingand energy absorption from the noise. Since the damping is weak, the groundstate phase space density should predominantly be a function of the conservedquantities, energy and angular momentum.  A candidate for this phase space density is constructed for ground state ofthe relativistic hydrogen problem of a spinless particle. The first excitedstates and their spherical harmonics are also considered in this framework. Theanalytic expression of the ground state energy can be reproduced, providedaverages of certain products are replaced by products of averages. Thisanalysis puts forward that quantum mechanics may arise from an underlyingclassical level as a slow variable theory, where each new quantum operatorrelates to a new, well separated time interval.Comment: 15pages AIP tex with 1 Figur

Classical Phase Space Density for the Relativistic Hydrogen Atom