The one-dimensional Schr ¨odinger equation
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 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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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
... Abstract. We study the Aharonov–Bohm effect (AB effect) in quan- tum resonances for magnetic scattering in two dimensions. The system consists of four scatters, two obstacles and two scalar potentials with compact ...
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OF MAGNETIC SCHR ¨ ODINGER OPERATORS
... Abstract. We study the Aharonov–Bohm effect (AB effect) in quan- tum resonances for magnetic scattering in two dimensions. The system consists of four scatters, two obstacles and two scalar potentials with compact ...
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Algorithm for computing a wave packet evolution of the time-dependent Schr¨ odinger equation
... the one- dimensional 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 ...
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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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SCHR ¨ ODINGER OPERATORS IN TWO DIMENSIONS
... scatterers, one bounded obsta- cle and two scalar potentials with compact supports at large separation, and the magnetic field is completely shielded by the obstacle placed between the two supports of the scalar ...
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A NUMERICAL STUDY OF SCHR ODINGER EQUATION COUPLED WITH NEWTONIAN GRAVITY APPROVED BY DISSERTATION COMMITTEE:
... As one sees, the matter distribution begins to atten out as in the rst movie, but the larger angular velocity forces more matter out to the computational bound- ...in one spatial ...
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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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Localisation of Low Energy Eigenfunctions to the Schr ?odinger Operator
... eigenfunctions of L in this subset) with eigenvalue λ ± δ. For these subsets to exist, 1 u needs to vary substantially. Since u solves Lu = 1, this phenomena cannot occur when V is smooth, and does not vary ...
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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 Coupled Discrete Nonlinear Schr¨odinger Equations
... Nonlinear Schr¨ odinger Equations Shih-Feng Shieh ∗ Abstract —In this paper, we study the spatial disorder of coupled discrete nonlinear Schr¨ odinger (CDNLS) equations with piecewise-monotone ...
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THE ESSENTIAL SELF-ADJOINTNESS OF SCHR ¨ ODINGER OPERATORS WITH OSCILLATING POTENTIALS
... The expression above effectively describes the time it takes for a particle under the influence of the potential V to move from the origin to infinity. On the one hand, if V (x) ≥ −x 2 − b, then this quantity will ...
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First eigenvalue of Schr¨ odinger operator of space-like hypersurfaces
... 1 Introduction E84 1 Introduction Space-like hypersurfaces with constant mean curvature or constant scalar curvature in an arbitrary Lorentz manifold play an important role in gen- eral relativity. Space-like ...
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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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Spatial Disorder of Soliton Solutions for 2D Nonlinear Schr¨odinger Lattices
... Nonlinear Schr¨odinger Lattices Shih-Feng Shieh Abstract—In this paper, we employ the construction of topo- logical horseshoes to study the pattern of the soliton solutions to the discrete nonlinear ...
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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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