Introduction to the Postulates of Quantum Mechanics

Mikio Nakahara

Quantum mechanics is founded on several postulates, which cannot be proven theoretically. They are justified only through an empirical fact that they are consistent with all the known experimental results. The choice of the postulates depends heavily on authors’ taste. Here we give one that turns out to be the most convenient in the study of quantum information and computation. For a general introduction to quantum mechanics, we recommend [1, 2, 3, 4], for example. [5] and [6] contain more advanced subjects than those treated in this chapter.

Alberto Galindo, P. Pascual

Renato Portugal

T. Buch

The shock to which students approaching quantum mechanics for the first time are exposed by the introduction of the postulates on which the mathematical framework of the theory is based, can be much smoothed by a discussion of a semiphilosophical nature about the connection between mathematical theories and the physical reality they are supposed to explain. The general outline of such a discussion is presented, with the purpose of making the introduction of operators to represent physical magnitudes more plausible to the students.

Yasser Omar

In this article, we discuss the identity and indistinguishability of quantum systems and the consequent need to introduce an extra postulate in Quantum Mechanics to correctly describe situations involving indistinguishable particles. This is, for electrons, the Pauli Exclusion Principle, or in general, the Symmetrization Postulate. Then, we introduce fermions and bosons and the distributions respectively describing their statistical behaviour in indistinguishable situations. Following that, we discuss the spin-statistics connection, as well as alternative statistics and experimental evidence for all these results, including the use of bunching and antibunching of particles emerging from a beam splitter as a signature for some bosonic or fermionic states.

Ajit Kumar