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A duality between an electrostatic problem in a three dimensional world and a quantum mechanical problem in a one dimensional world which allows one to obtain the ground state solution of the Schrodinger equation by using electrostatic results is generalized to three dimensions. Here, it is demonstrated that the same transformation technique is also applicable to the s-wave Schrodinger equation in three dimensions for central potentials. This approach leads to a general relationship between the electrostatic potential and the s-wave function and the electric energy density to the quantum mechanical energy.
The compressible Navier-Stokes-Poisson system is concerned in the present paper, and the global existence and uniqueness of the strong solution is shown in the framework of hybrid Besov spaces in three and higher dimensions.
A version of the twisted Poincar{e} duality is proved between the Poisson homology and cohomology of a polynomial Poisson algebra with values in an arbitrary Poisson module. The duality is achieved by twisting the Poisson module structure in a canoni
By starting from the stochastic Schrodinger equation and quantum trajectory theory, we introduce memory effects by considering stochastic adapted coefficients. As an example of a natural non-Markovian extension of the theory of white noise quantum tr
The equivalence between Chern-Simons and Einstein-Hilbert actions in three dimensions established by A.~Achucarro and P.~K.~Townsend (1986) and E.~Witten (1988) is generalized to the off-shell case. The technique is also generalized to the Yang-Mills
We obtain novel nonlinear Schr{o}dinger-Pauli equations through a formal non-relativistic limit of appropriately constructed nonlinear Dirac equations. This procedure automatically provides a physical regularisation of potential singularities brought