In this paper we are dealing with fundamental problems in quantum mechanics. The problem is related to the question of whether there is a connection between the phase and the amplitude of the wave function and the conditions under which this relationship exists. To deal with the problems we work within the framework of a specific model of particle in an infinite potential well with a central barrier.  We have shown that in domains near the barrier the amplitude and phase can be calculated from each other since the conditions of log analytical uncertainty hold. These issues were discussed in light of quantum theory and previous literature. 

[1]  A. Yahalom & R. Englman, "Phase-Modulus Relations for a Reflected Particle”, J. Phys. Chem. A, 107 (37), 7170 - 7174 (2003). [Los-Alamos Archives -quant-ph/0406197]