Summary: In contrast to the classical Hamiltonian mechanics whose chaotic behaviors are now well established, quantum mechanics is still obscure about the origin of its random behavior. It is shown in this paper that in case of the stadium billiard, the fact that the nodal lines are smooth but are randomly oscillating, as first described by Heller, and MacDonald and Kaufman, can be interpreted as due to the irregular pseudochaotic behavior of the phase. To do this, we employ the path integral representation of propagator and the reinterpreted Bohm's formulation of quantum mechanics. Thus we reach the conclusion that although the chaotic behavior in quantum mechanics is suppressed by the Einstein quantization condition, it is observed in the properly defined phase of the propagator, or of the wave function, as a pseudochaos. In other words quantum mechanics has the counterpart of classical chaos in the phase of the propagator, and consequently, the wave function is also, pseudochaotic (random) with respect to q, but it does not exhibit exponential instability. The essential feature of quantum chaos manifests itself in the vanishings of the average of the wave function and the two-point correlation of the wave function at high energies. They are closely related to ergodicity and quantum measurement, and in particular new light will be shed on the measurement theory. The basic assumptions in the random matrix theory are discussed, confirming the universality of level spacing distribution.