A New Answer to Pauli's Question: Almost All Quantum States Can Be Uniquely Determined by Measuring Location and Momentum
Donald A. Jackson, Olga M. Kosheleva · scholarworks - UTEP (The University of Texas at El Paso) · 2010
In classical mechanics, we can uniquely reconstruct the state of each particle by measuring its spatial location and momentum. In his 1958 paper, W. Pauli, one of the founders of quantum mechanics, conjectured that the same should be true in the quantum case as well: that every quantum state can be uniquely determined by measuring spatial location and momentum. This conjecture was disproven: there are pairs of physically different states that cannot be distinguished if we only measure special location and momentum. A natural question is: how frequent are such pairs? In this paper, we show that almost all quantum states can be uniquely reconstructed by measuring spatial location and momentum. Thus, in practice, Pauli's conjecture is true.