|
| related topics |
| {temperature, thermal, energy} |
| {particle, mechanics, theory} |
| {energy, state, states} |
| {trap, ion, state} |
| {field, particle, equation} |
| {cavity, atom, atoms} |
| {cos, sin, state} |
| {state, phys, rev} |
| {state, states, entangled} |
|
Untouched aspects of the wave mechanics of a particle in one dimensional
box
Yatendra S. Jain
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.
- oai_identifier:
- oai:arXiv.org:quant-ph/0606009
- categories:
- quant-ph
- comments:
- 8 pages no figure
- arxiv_id:
- quant-ph/0606009
- created:
- 2006-06-01
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