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Fractional revivals of wave packets in an infinite square well are scrutinized with a viewpoint rooted in Fourier analysis, and a compact relation, expressing the wavefunction Ψ(x,t) for certain values of t in terms of spatially displaced copies of Ψ(x,0), is derived without appealing to a classical analogy; conditions for the appearance of an interference pattern in a plot of the position probability density of a wave packet are deduced, along with related results obtained previously from different considerations, with minimal effort. The specific case of a packet of Gaussian shape is analysed in greater detail to provide concrete illustrations of fractional revivals with or without interference between overlapping copies of wave packets, depending on whether a finite value of the so-called classical time can or cannot be assigned to the wave packet.

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Heat transfer through a semiconductor or dielectric thin film is investigated by using the single relaxation time approximation to the Boltzmann equation. The radiance is expanded in terms of the Laguerre polynomial with time as argument, and the ensuing time-independent equation is solved with the aid of the Galerkin technique. Films of different thicknesses, ranging from 0.01 to 10 mean free paths, have been considered. The results, calculated for different time, ranging from 0.01 to 10 relaxation times, are presented in the forms of the following quantities (in dimensionless units): the temperature (normalized dimensionless internal energy), the heat flux, and the irradiance. Differences between the results obtained by this approach and those found by solving partial differential equations of heat conduction (Fourier's Law and Cattaneo's equation) are noted.

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