The fractional Schrdinger equation and the infinite potential well-numerical results using the Riesz derivativedoi:10.1007/978-3-642-33335-4_10001Richard Herrmann
Caglioti E., Caprino S., Marchioro C., Pulvirenti M.: The Vlasov equa- tion with infinite mass. Arch. Ration. Mech. Anal. 159, 85-108 (2001)Caglioti, E., Carprino, S., Marchioro, C., and Pulvirenti, M., The Vlasov equation with infinite mass, Arch. Rational Mech. Anal, 159...
Infinite time blow-up for the three dimensional energy critical heat equation in bounded domains doi:10.1007/s00208-024-02885-xWe consider the Dirichlet problem for the energy-critical heat equationut=Δu+u5inΩ×R+,u=0onΩ×R+,u(x,0)=u0(x)inΩ,\\documentclass[12pt]{minimal} \\use...
2.2 The infinite square well V\left( x \right) =\left\{ \begin{array}{c} 0, \mathrm{if} 0\le x\le a,\\ \infty , \mathrm{otherwise}.\\ \end{array} \right. In side the well, the time-independent \mathrm{Schr\ddot odinger} equation reads -\frac{\hbar ^2}{2m}\frac{d...
atoms are not conservative.) Equation (40.3), known as Boltzmann's law, is another of the principles of statistical mechanics: that the probability of finding molecules in a given spatial arrangement varies exponentially with the negative of the potential energy of that arrangement, divided by kT...
(1974) The infinite dimensional Riccati equation. J. Math. Anal. & Appl. 47: pp. 43-57A. J. Pritchard, R. F. Curtain, The infinite dimensional Riccati equation, J. Math. Anal. and Appl. 47, xxx (1974).Curtain, R.F., Pritchard, A.J., The infinite-dimensional Riccati equation, ...
Various thermodynamic quantities can be derived from excess internal energyu(ρ,β). This energy is defined by the following equation. u(ρ,β)=2πρ2∫0∞drr2ϕ(r)g(r). (1) Here,β=1/kT, andg(r) is a distribution function. The thermodynamic potential is clearly related to the ...
Huygens' Principle (1678) implies that every point on a wave front serves as a source of secondary wavelets, and the new wave front is the tangential surface to all the secondary wavelets. But two problems arise: portions of wavelets that exist outside o
where space charge densityρis also zero here. The above formulas could be used to calculate the stationary space potential, as shown in Fig.6a, c, and it could clearly be seen that during the contact-separation process, the electrical potential decayed with distance, and the voltage difference...
Painlevé functions show up already ingauge theory, namely matrix models. The most famous example appears in the analysis of the Hermitian matrix model with cubic potential of Kontsevich and Painlevé I equation [5]. As an important fact, the full matrix model partition function has been identifie...