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

Original · EN

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 ψₖ(r) (representing the relative motion of two particles), (ii) the expectation value of hard core (HC) repulsion (<VHC(r)>), (iii) the inconsistency of the statements, r ≤σand ψₖ(r ≤σ)=0 (σ=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 <VHC(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 VHC(r), to satisfy q ≥π/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.