Abstract
The recently developed quantum surface of section method is applied to a search for extremely high-lying energy levels in a simple but generic Hamiltonian system between integrability and chaos, namely the semiseparable 2-dim oscillator. Using the stretch of 13,445 consecutive levels with the sequential number around $1.8\cdot 10^7$ (eighteen million) we have clearly demonstrated the validity of the semiclassical Berry-Robnik level spacing distribution while at 1000 times smaller sequential quantum numbers we find the very persistent quasi universal phenomenon of power-law level repulsion which is globally very well described by the Brody distribution.
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