The State of a Physical System

Yoshifumi Ito

In this paper, we study the phenomena of potential well of infinite depth on the view point of natural statistical physics. The mathematical model of this physical system is the system of micro-particles moving periodically with constant velocity in the interval D = [−a, a], (a > 0). Thereby we obtain the structure of this physical system at the stationary state. Thus we clarify that this physical system is the composed state of the proper physical systems at the stationary state and the ratio of their composition is given by the sequence {|an|2}n=0 ∪ {|bn|2}∞n=1, where an, (n ≥ 0) and bn, (n ≥ 1) are the Fourier type coefficients of the initial state ψ ∈ L2. Then we obtain the energy expectation of the total physical system Ē =∞Σn=0 n2π2ℏ2/2ma2 (|an|2 + |bn|2), where m denotes the mass of one micro-particle.

Roger G. Newton

Richard Healey

Often a pair of quantum systems may be represented mathematically (by a vector) in a way each system alone cannot: the mathematical representation of the pair is said to be non-separable: Schrödinger called this feature of quantum theory entanglement. It would reflect a physical relation between a pair of systems only if a system’s mathematical representation were to describe its physical condition. Einstein and colleagues used an entangled state to argue that its quantum state does not completely describe the physical condition of a system to which it is assigned. A single physical system may be assigned a non-separable quantum state, as may a large number of systems, including electrons, photons, and ions. The GHZ state is an example of an entangled polarization state that may be assigned to three photons.

Andrzej Posiewnik

Krystyna Bugajska, Slawomir Bugajski

Michel Paty

Despite its power as the conceptual basis for a huge range of physical phenomena in atomic and subatomic physics, quantum mechanics still suffers from a lack of clarity regarding the physical meaning of its fundamental theoretical concepts, such as those of quantum state and of quantum theoretical quantities or variables , dealt with by the known mathematical-theoretical rules. These concepts have generally been considered as not giving a direct description of physical systems, for they do not correspond to what is usually understood by `physical states' or `physical properties', notably characterized by definite numerical values such as those obtained from measurement. The situation has been tentatively expressed in terms of various `interpretations', conceived not only with regard to the physical meanings of mathematical quantities, but also in connection with philosophical statements about `physical reality'. The question of whether or not quantum theoretical quantities describe definite physical systems existing in nature has therefore generally been considered as beyond the possibilities of physics, because of the definitions that are commonly taken for `physical state' and `physical quantity'. We sketch the main ideas on this problem and propose a possible way out of the puzzle, in terms of an extension of the meaning given to the concepts of the physical state and physical quantity of a system, which would allow one, without any theoretical change in quantum mechanics, to speak consistently of real quantum systems as having definite physical properties .