Wave Mechanics of Two Hard Core Quantum Particles in 1-D Box

Details Wave Mechanics of Two Hard Core Quantum Particles in 1-D Box Wave Mechanics of Two Hard Core Quantum Particles in 1-D Box

2006-03-26

arxiv.org/abs/quant-ph/0603233v1

Central European J. Phys. 2(4) 2004, 709-719

Physics

Quantum Physics

12 pages, no figure

Scientific paper

The wave mechanics of two impenetrable hard core particles in 1-D box is analyzed. Each particle in the box behaves like an independent entity represented by a {\it macro-orbital} (a kind of pair waveform). While the expectation value of their interaction, $$, vanishes for every state of two particles, the expectation value of their relative separation, $$, satisfies $ \ge \lambda/2$ (or $q \ge \pi/d$, 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 $ = \lambda/2$, phase position separation $\Delta\phi = 2\pi$ and momentum $|q_o| = \pi/d$) and experience a mutual repulsive force ({\it zero point repulsion}) $f_o = h^2/2md^3$ 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 the correct microscopic understanding of widely different many body systems.

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