Basic Problems of a Microscopic Theory of a Many Body Quantum System

TL;DR

This paper critically examines the wave mechanics of two hard core quantum particles, revealing new insights into their interactions and proposing a novel approach to develop more accurate microscopic theories for many-body quantum systems.

Contribution

It introduces a new perspective on the wave mechanics of two particles, challenging established views on HC repulsion and phase correlation, and applies this to improve theories of interacting bosons and fermions.

Findings

<V_{HC}(r)> is zero, contrary to previous beliefs

System of interacting bosons may have (q, -q) pair condensation

Dominance of interparticle phase correlation at low temperatures

Abstract

Basic problems of a microscopic theory of many body quantum systems and different aspects of a new approach which can help in solving them are discussed in detail. To this effect we make a critical study of the wave mechanics of two hard core quantum particles and discover its several untouched aspects, viz.: (i) the useful details of \psi_k(r) (representing the relative motion of two particles), (ii) the expectation value of hard core (HC) repulsion (<V_{HC}(r)>), (iii) the inconsistency of the statements, r \le\sigma and \psi_k(r \le\sigma)=0 (\sigma=HC diameter of a particle), with uncertainty principle particularly for low k values, (iv) the lower bound of allowed values of k=2q, (v) the dominance of interparticle phase correlation in low temperature phase. For the first time this study concludes that <V_{HC}(r)> has zero value which does not agree with its non-zero value known for the last several decades. This also finds compelling reasons for a system of interacting bosons such as liquid ^4He to have (q, -q) pair condensation with allowed q, obviously controlled by V_{HC}(r), to satisfy q \ge\pi/d. Several important aspects of N body quantum systems like liquids ^4He and ^3He are also concluded. Free from any error [see editor's note J. Scientific Exploration 16(1), p.1 (2002)], our approach can help in developing nearly exact microscopic theories of widely different systems of interacting bosons and fermions, as demonstrated for liquids ^4He type systems [J. Scientific Exploration, 16, 77-116 (2002)]. The paper also sums up the expert observations with our response to facilitate one to have a critical assessment and better understanding of the new approach.