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Full-Text Articles in Physics
Complex Energies And The Lambert W Function, A Das, B.G. Sidharth, K. Roberts, Sree Ram Valluri
Complex Energies And The Lambert W Function, A Das, B.G. Sidharth, K. Roberts, Sree Ram Valluri
Physics and Astronomy Publications
We apply the Lambert W function in the context of complex energy values in statistical systems of fermions and bosons. We derive the condition for the transformation connecting fermions and bosons. We discuss the physical significance of these results and investigate the conditions under which bosonization effects take place. The fermion and boson statistical and structural distributions discussed in this work suggest the possibility of their extensions to generalized Planck distributions.
Lambert W Function Methods In Double Square Well And Waveguide Problems, Narola Harsh Bharatbhai, P C Deshmukh, Robert B. Scott, Ken Roberts, Sree Ram Valluri
Lambert W Function Methods In Double Square Well And Waveguide Problems, Narola Harsh Bharatbhai, P C Deshmukh, Robert B. Scott, Ken Roberts, Sree Ram Valluri
Physics and Astronomy Publications
Using methods related to the Lambert W function, we present solutions of two apparently different problems: (1) The one-dimensional double square well potential in quantum mechanics and (2) The transverse electric and magnetic modes for a step-index electromagnetic waveguide. The solution techniques provide insight into the bound energy states for the single and double square well problems and the allowed modes of propagation in a waveguide with varying refractive indices. The solutions can be viewed in either of two related complex plane representations. Comparison of the solution geometries suggests that interesting applications may be possible in nanostructures and devices which …
Tutorial: The Quantum Finite Square Well And The Lambert W Function, Sree Ram Valluri, Ken Roberts
Tutorial: The Quantum Finite Square Well And The Lambert W Function, Sree Ram Valluri, Ken Roberts
Physics and Astronomy Publications
We present a solution of the quantum mechanics problem of the allowable energy levels of a bound particle in a one-dimensional finite square well. The method is a geometric-analytic technique utilizing the conformal mapping w -> z = we(w) between two complex domains. The solution of the finite square well problem can be seen to be described by the images of simple geometric shapes, lines, and circles, under this map and its inverse image. The technique can also be described using the Lambert W function. One can work in either of the complex domains, thereby obtaining additional insight into the …
D-Dimensional Bose Gases And The Lambert W Function, Sree Ram Valluri, J Tanguay, M Gil, D J. Jeffrey
D-Dimensional Bose Gases And The Lambert W Function, Sree Ram Valluri, J Tanguay, M Gil, D J. Jeffrey
Physics and Astronomy Publications
The applications of the Lambert W function (also known as the W function) to D-dimensional Bose gases are presented. We introduce two sets of families of logarithmic transcendental equations that occur frequently in thermodynamics and statistical mechanics and present their solution in terms of the W function. The low temperature T behavior of free ideal Bose gases is considered in three and four dimensions. It is shown that near condensation in four dimensions, the chemical potential μ and pressure P can be expressed in terms of T through the W function. The low T behavior of one- and two-dimensional ideal …
The Lambert W Function And Quantum Statistics, Sree Ram Valluri, M. Gil, D. J. Jeffrey, Shantanu Basu
The Lambert W Function And Quantum Statistics, Sree Ram Valluri, M. Gil, D. J. Jeffrey, Shantanu Basu
Physics and Astronomy Publications
We present some applications of the Lambert W function (W function) to the formalism of quantum statistics (QS). We consider the problem of finding extrema in terms of energy for a general QS distribution, which involves the solution of a transcendental equation in terms of the W function. We then present some applications of this formula including Bose–Einstein systems in d dimensions, Maxwell–Boltzmann systems, and black body radiation. We also show that for the appropriate parameter values, this formula reduces to an analytic expression in connection with Wien’s displacement law that was found in a previous study. In addition, we …