  We are experimentally investigating possible violations of standard quantum
mechanics predictions in the Gran Sasso underground laboratory in Italy. We
test with high precision the Pauli Exclusion Principle and the collapse of the
wave function (collapse models). We present our method of searching for
possible small violations of the Pauli Exclusion Principle (PEP) for electrons,
through the search for anomalous X-ray transitions in copper atoms. These
transitions are produced by new electrons (brought inside the copper bar by
circulating current) which can have the possibility to undergo Pauli-forbidden
transition to the 1s level already occupied by two electrons. We describe the
VIP2 (VIolation of the Pauli Exclusion Principle) experimental data taking at
the Gran Sasso underground laboratories. The goal of VIP2 is to test the PEP
for electrons in agreement with the Messiah-Greenberg superselection rule with
unprecedented accuracy, down to a limit in the probability that PEP is violated
at the level of 10E-31. We show preliminary experimental results and discuss
implications of a possible violation.
