In the VIP2 (VIolation of the Pauli Exlusion Principle) experiment at the Gran Sasso underground laboratory (LNGS) we are searching for possible violations of standard quantum mechanics predictions. With high precision we investigate the Pauli Exclusion Principle and the collapse of the wave function (collapse models). We will present our experimental method of searching for possible small violations of the Pauli Exclusion Principle for electrons, via the search for anomalous X-ray transitions in copper atoms, produced by new electrons (brought inside a copper bar by circulating current) which could have the probability to undergo Pauli-forbidden transition to the ground state (1 s level) already occupied by two electrons. We will describe the concept of the VIP2 experiment taking data at LNGS presently. The goal of VIP2 is to test the PEP for electrons with unprecedented accuracy, down to a limit in the probability that PEP is violated at the level of 10$^{-31}$. We will show preliminary experimental results obtained at LNGS and discuss implications of a possible violation.
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