arXiv quant-ph/06032332006-03-26quant-ph

一维盒子中两个硬核量子粒子的波动力学

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

Yatendra S. Jain

备注：: 12 pages, no figure
发表信息：: Central European J. Phys. 2(4) 2004, 709-719
DOI：: 10.2478/BF02475571

摘要：

分析了一维盒子中两个不可穿透硬核粒子的波动力学。盒子中的每个粒子都表现得像一个独立的实体，由{ \it macro-orbital}（一种成对波形）表示。当两个粒子的相互作用的期望值$<V_{HC}(x)>$对于两个粒子的每个状态为零时，它们的相对分离的期望值$<x>$满足$<x> \ge λ/2$（或$q \ge π/d$，其中$2d = L$是盒子的大小）。处于基态的粒子定义了它们的波包的紧密排列（具有$<x> = λ/2$、相位分离$Δϕ= 2π$和动量$|q_o| = π/d$），并经历了相互排斥力（{ \it零点排斥}）$f_o = h^2/2md^3$，这也试图扩大盒子。虽然两个粒子在激发态的相对动力学代表了通常的碰撞运动，但在基态的相对动力学则是无碰撞的。这些结果在确定对广泛不同的许多身体系统的正确微观理解方面具有重要意义。

英文摘要：

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, $<V_{HC}(x)>$, vanishes for every state of two particles, the expectation value of their relative separation, $<x>$, satisfies $<x> \ge λ/2$ (or $q \ge π/d$, 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 $|q_o| = π/d$) 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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英文摘要：

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