Solving the coupled Schr¨ odinger equation
A Schr¨odinger Equation for Solving the Riemann Hypothesis
... resulting Schr¨ odinger equation is performed, and a convergent solution for the nontrivial zeros of the analytic continuation of the Riemann zeta function is ...
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Schr¨odinger Equation and the Quantization of Celestial Systems
... generalize Schr ¨odinger equation to describe quantization of celestial ...of Schr¨odinger equation from Gross-Pitaevskii-Ginzburg equation, which supports this superfluid ...
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A NUMERICAL STUDY OF SCHR ODINGER EQUATION COUPLED WITH NEWTONIAN GRAVITY APPROVED BY DISSERTATION COMMITTEE:
... the Schrodinger and Newtonian grav- ity equations lead to added algorithm ...in solving this coupled system of ...for solving time dependent problem are usually implicitmethods which ...
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Spatial Disorder Of Coupled Discrete Nonlinear Schr¨odinger Equations
... Of Coupled Discrete Nonlinear Schr¨ odinger Equations Shih-Feng Shieh ∗ Abstract —In this paper, we study the spatial disorder of coupled discrete nonlinear Schr¨ odinger (CDNLS) ...
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Numerical Solution of Time-Dependent Gravitational Schr ¨odinger Equation
... gravitational Schr¨odinger equation, including Rubcic & Rubcic’s method and also Nottale’s Scale Relativity ...gravitational Schr ¨odinger equation ...gravitational ...
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Covariance of the Schr¨ odinger equation under low velocity boosts.
... that Schr¨odinger wave functions are not covari- ant under Galilean ...the Schr¨odinger group and claim Galilean invariance of the Schr¨odinger wave ...the ...
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ANALYTICAL AND NUMERICAL ASPECTS OF THE DISSIPATIVE NONLINEAR SCHRODINGER EQUATION
... nonlinear Schr¨ odinger equation (d-NLS equation) are ...d-NLS equation is introduced in order to make ...d-NLS equation and the analytical solutions are compared with the ...
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OF MAGNETIC SCHR ¨ ODINGER OPERATORS
... 3.2. We are now in a position to prove the main theorem. The lemma below is proved in almost the same way as in the proof of [7, Lemma 4.6]. We skip its proof. Lemma 3.5. Assume the same assumptions as in Theorem 1.1. ...
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Algorithm for computing a wave packet evolution of the time-dependent Schr¨ odinger equation
... time-dependent Schr¨ odinger equation on a finite time interval is pre- ...time-dependent Schr¨ odinger equa- tion for the P¨ oschl-Teller two-center problem is used to illustrate an ...
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Schr¨odinger Equation for a Half Spin Electron in a Time Dependent Magnetic Field
... We now deal with time-independent ˜θ and time-dependent ˜ φ, so that ˜θ = θ = constant. As eigenvalues of the operator C we get (see the last page for equation (38)), which correspond to the energies of the lower ...
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Krylov Subspace Spectral Methods for the Time-Dependent Schr¨odinger Equation with Non-Smooth Potentials
... Abstract—This paper presents modifications of Krylov Subspace Spectral (KSS) Methods, which build on the work of Gene Golub and others per- taining to moments and Gaussian quadrature to pro- duce high-order accurate ...
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Statistical Mechanics-based Schr¨odinger treatment of Gravity
... simple Schr¨ odinger mechanism was utilized, in which his celebrated equation is solved with a potential function based on the microscopic Verlinde’s entropic force advanced in [Physica A 511 (2018) ...
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Spatial Disorder of Soliton Solutions for 2D Nonlinear Schr¨odinger Lattices
... by the construction of homoclinic/hetronic orbits. In [26], the spatial disorder in the one-dimensional NLS equations equipped with periodic/quasiperiodic trapped potentials was studied, in which a coherent structure ...
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Existence of Fractional Stochastic Schr¨odinger Evolution Equations with Potential and Optimal Controls
... Z. Yan and X. Jia are with the Department of Mathematics, Hexi Univer- sity, Zhangye, Gansu 734000, P.R. China, e-mail: [email protected]. Schr¨odinger equation for delta potentials. Wang et al. [17] ...
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Coupled Method for Solving Time-Fractional Navier-Stokes Equation
... Abstract— This paper witnesses the coupling of two basic transforms: the He-Laplace transform (HLT) which is a blend of Laplace transformation and Homotopy perturbation methods and the fractional complex transform (FCT). ...
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Numerical solution of elliptic boundary-value problems for Schr¨ odinger-type equations using the Kantorovich method
... for Schr¨ odinger-type equations based on Kantorovich method that re- duces the initial problem to a set of boundary-value problems for a system of ordinary second-order differential equations are ...3D ...
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On the scattering theory for the cubic nonlinear. one space dimension. Schr\"odinger and Hartree type equations in. 1.
... \{ iu_{t}+ \frac{1}{2}u_{xx}=f(|u|^{2})u , (t, x)\in R^{2} u(0, x)=u_{0}(x) , x\in R , where the nonlinear interaction term is f(|u|^{2})=V*|u|^{2} , V(x)=\lambda|x|^{-\delta} , \lambda\in R , 0<\delta<1 in the ...
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A Multilevel Method for Solving Neutron Kinetics Equations Coupled with the Heat Transfer Equation.
... Chapter 1 Introduction A nuclear reactor core is a sophisticated multiphysics system governed by complex thermo- mechanical processes within the materials present in the core. To perform a successful design and accurate ...
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ALGORITHM FOR SOLVING A GENERALIZED HIROTA-SATSUMA COUPLED KDV EQUATION USING HOMOTOPY PERTURBATION TRANSFORM METHOD
... Hirota-Satsuma Coupled KdV ...Hirota-Satsuma Coupled KdV equation without using Adomian’s polynomials which can be considered as a clear advantage over the decomposition ...
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Solving the Vlasov equation in complex geometries
... when modeling nonlinear phenomena such as turbulence, which is usually studied in the fusion community through the development of gyrokinetic codes [12]. These first-principle codes solve a coupled Vlasov-Poisson ...
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