(2004). The Break Down of Semiclassical Density Matrix of a Particle Moving in Barrier Potential at Temperature T. test, 27(1), 53-64. doi: 10.21608/ejs.2004.149311
. "The Break Down of Semiclassical Density Matrix of a Particle Moving in Barrier Potential at Temperature T". test, 27, 1, 2004, 53-64. doi: 10.21608/ejs.2004.149311
(2004). 'The Break Down of Semiclassical Density Matrix of a Particle Moving in Barrier Potential at Temperature T', test, 27(1), pp. 53-64. doi: 10.21608/ejs.2004.149311
The Break Down of Semiclassical Density Matrix of a Particle Moving in Barrier Potential at Temperature T. test, 2004; 27(1): 53-64. doi: 10.21608/ejs.2004.149311

The Break Down of Semiclassical Density Matrix of a Particle Moving in Barrier Potential at Temperature T

Egyptian Journal of Solids
Article 5, Volume 27, Issue 1, 2004, Pages 53-64    PDF (309.6 K)
DOI: 10.21608/ejs.2004.149311
Abstract
The nonlinear barrier potential with bound states is presented. The
equilibrium density matrix of a particle moving at temperature T in this
nonlinear barrier potential field is determined. The exact density matrix is
compared with the result of the path integral approach in the semiclassical
approximation is found to be sufficient at high temperatures while at low
temperatures the fluctuation paths may have a caustic depending on
temperature and end points. Near the caustics, the divergence of the simple
semicalssical approximation of the density matrix is removed by a nonlinear
fluctuation potential. For opaque barriers, the improved semiclassical
approximation is compulsory required.
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