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