Postulate 2

Michele Cini

Ram Yatan Prasad, Pranita

This chapter starts with the definition of postulates. Here, in quantum mechanics, the postulates concern the atomic and molecular properties, which are quite far removed from everyday experience. The postulates described here make no claim to those happy mathematical adjectives such as ‘rigorous’, ‘complete’, or irreducible. The ‘proof’ of the postulates is their ability to explain the adequate experimental observations. Here, we have incorporated six postulates. The first postulate opines that ‘the state of quantum mechanical objects is described by a wavefunction’, whereas the second postulate says that ‘every physical observable is expressed by a linear operator’. It also describes how a quantum mechanical operator is constructed. The third postulate gives an idea that the measurement of a physical observable will yield a result, which is one of the Eigen values of the corresponding operator for that observable. The fourth postulate gives how the average of a sequence of measurement is connected with an operator. The fifth postulate is called the time-dependent postulate. Here, it gives a relationship between the time-dependent wave function and an operator, whereas the sixth postulate says that the wave function must be antisymmetric (or symmetric) for the exchange of identical fermions. It must be noted that each and every postulate has been explained clearly. The references, solved problems, and questions on concepts have been given at the end of the chapter.

Valia Allori

A common way of characterizing Boltzmann’s explanation of thermodynamics in term of statistical mechanics is with reference to three ingredients: the dynamics, the past hypothesis, and the statistical postulate. In this paper I focus on the statistical postulate, and I have three aims. First, I wish to argue that regarding the statistical postulate as a probability postulate may be too strong: a postulate about typicality would be enough. Second, I wish to show that there is no need to postulate anything, for the typicality postulate can be suitably derived from the dynamics. Finally, I discuss how the attempts to give preference to certain stochastic quantum theories (such as the spontaneous collapse theory) over deterministic alternatives on the basis that they do not need the statistical postulate fail.

Michele Cini

Oscar Diego

In this paper we are going to introduce a new dynamical postulate in Quantum Mechanics. This new principle is defined using path integrals over the set of normalized wave functions. We will show in a qualitative way that this postulate is equivalent to the Schrodinger equation and to the measurement postulates. Then we propose a new set of fundamental postulates for Quantum Mechanics. In this approach to Quantum Mechanics we separate the fundamental postulates and the physical interpretation. The fundamental postulates are abstract mathematical principles. Their physical interpretation depend on the physical system under study. These postulates do not use the concepts of measurement device and observer.

Michele Cini