dorsal/arxiv
View SchemaUntouched aspects of the wave mechanics of a particle in one dimensional box
| Authors | Yatendra S. Jain |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0606009 |
| URL | https://arxiv.org/abs/quant-ph/0606009 |
Abstract
Wave mechanics of a particle in 1-D box (size $= d$) is critically analyzed to reveal its untouched aspects. When the particle rests in its ground state, its zero-point force ($F_o$) produces non-zero strain by modifying the box size from $d$ to $d' = d + \Delta d$ in all practical situations where the force ($F_a$) restoring $d$ is not infinitely strong. Assuming that $F_a$ originates from a potential $\propto x^2$ ($x$ being a small change in $d$), we find that: (i) the particle and strained box assume a mutually bound state (under the equilibrium between $F_o$ and $F_a$) with binding energy $\Delta{E} = -\epsilon_o'\Delta{d}/d'$ (with $\epsilon_o' = h^2/8md'^2$ being the ground state energy of the particle in the strained box), (ii) the box size oscillates around $d'$ when the said equilibrium is disturbed, (iii) an exchange of energy between the particle and the strained box occurs during such oscillations, and (iv) the particle, having collisional motion in its excited states, assumes collisionless motion in its ground state. These aspects have desired experimental support and proven relevance for understanding the physics of widely different systems such as quantum dots, quantum wires, trapped single particle/ion, clusters of particles, superconductors, superfluids, {\it etc.} It is emphasized that the physics of such a system in its low energy states can be truly revealed if the theory incorporates $F_o$ and related aspects.
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"abstract": "Wave mechanics of a particle in 1-D box (size $= d$) is critically analyzed\nto reveal its untouched aspects. When the particle rests in its ground state,\nits zero-point force ($F_o$) produces non-zero strain by modifying the box size\nfrom $d$ to $d\u0027 = d + \\Delta d$ in all practical situations where the force\n($F_a$) restoring $d$ is not infinitely strong. Assuming that $F_a$ originates\nfrom a potential $\\propto x^2$ ($x$ being a small change in $d$), we find that:\n(i) the particle and strained box assume a mutually bound state (under the\nequilibrium between $F_o$ and $F_a$) with binding energy $\\Delta{E} =\n-\\epsilon_o\u0027\\Delta{d}/d\u0027$ (with $\\epsilon_o\u0027 = h^2/8md\u0027^2$ being the ground\nstate energy of the particle in the strained box), (ii) the box size oscillates\naround $d\u0027$ when the said equilibrium is disturbed, (iii) an exchange of energy\nbetween the particle and the strained box occurs during such oscillations, and\n(iv) the particle, having collisional motion in its excited states, assumes\ncollisionless motion in its ground state. These aspects have desired\nexperimental support and proven relevance for understanding the physics of\nwidely different systems such as quantum dots, quantum wires, trapped single\nparticle/ion, clusters of particles, superconductors, superfluids, {\\it etc.}\nIt is emphasized that the physics of such a system in its low energy states can\nbe truly revealed if the theory incorporates $F_o$ and related aspects.",
"arxiv_id": "quant-ph/0606009",
"authors": [
"Yatendra S. Jain"
],
"categories": [
"quant-ph"
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"title": "Untouched aspects of the wave mechanics of a particle in one dimensional box",
"url": "https://arxiv.org/abs/quant-ph/0606009"
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