Wave mechanics of two hard core quantum particles in A 1-D box

Abstract

The wave mechanics of two impenetrable hard core particles in a 1-D box is analyzed. Each particle in the box behaves like an independent entity represented by a macro-orbital (a kind of pair waveform). While the expectation value of their interaction, < VHC(x) >, vanishes for every state of two particles, the expectation value of their relative separation, < x >, satisfies < x > ≥ λ/2 (or q ≥ π/d, with 2d = L being the size of the box). The particles in their ground state define a close-packed arrangement of their wave packets (with < x > = λ/2, phase position separation Δφ = 2π and momentum qo = π/d) and experience a mutual repulsive force (zero point repulsion) fo = h2/2md3 which also tries to expand the box. While the relative dynamics of two particles in their excited states represents usual collisional motion, the same in their ground state becomes collisionless. These results have great significance in determining a correct microscopic understanding of widely direrent many-body systems. © Central European Science Journals. All rights reserved.