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Solution of the Two-Dimensional Time-Dependent Schrodinger Equation Applied to Nuclear Proton Decay

Abstract : A rigorous approach to study the temporal evolution of physical processes is to follow the development in time of a given initial state, by numerically solving the time-dependent Schrodinger equation. This represents a natural modeling of the dynamical behaviour. We considered the equation in two spatial coordinates, to describe deformed nuclear shapes. The Hamiltonian is discretized by special, functionally fitted difference formulae of the derivatives and then a Crank-Nicolson scheme is applied. The resulting linear system with large sparse matrix is solved by a variant of Conjugate Gradient Method. The numerical solution has been used to the description of the proton decay. We also discuss the treatment of numerical boundary conditions, the preparation of the initial wavefunction and the calculation of the decay rate through the flux.
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http://hal.in2p3.fr/in2p3-00464965
Contributor : Virginie Mas <>
Submitted on : Thursday, March 18, 2010 - 4:36:09 PM
Last modification on : Thursday, January 11, 2018 - 6:12:51 AM

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M. Rizea, N. Carjan. Solution of the Two-Dimensional Time-Dependent Schrodinger Equation Applied to Nuclear Proton Decay. International Conference on Numerical Analysis and Applied Mathematics (ICNAAM 2009), Sep 2009, Rethymno, Greece. pp.1582-1585, ⟨10.1063/1.3241407⟩. ⟨in2p3-00464965⟩

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