WebJun 4, 1998 · An explicit algorithm for the time‐stepping solution of the Schrödinger equation is described, which is second‐order accurate in time. It is a staggered‐time algorithm, in which the real and imaginary parts of the wave function are defined at alternate times. The method combines the speed and simplicity of explicit methods with the … WebFeb 25, 2024 · Stochastic logarithmic Schrodinger equations: energy regularized approach Jianbo Cui, Liying Sun In this paper, we prove the global existence and uniqueness of the solution of the stochastic logarithmic Schrödinger (SlogS) equation driven by additive noise or multiplicative noise.
Matlab Code For Solving Schrodinger Equation
WebMoreover, we write fb meaning that the Fourier transform is taken with respect to the spatial variable x. ... Sharp global well-posedness for a higher order Schrödinger equation, J. Fourier Anal. Appl., 12 (2006), pp. 53–70. [6] , On the ill-posedness for a nonlinear Schrödinger-Airy equation, Quart. Appl. Math., 71 (2013), pp. 267–281 ... WebThe nonlinear Fourier transform is eminently suited to address them – at least from a theoretical point of view. Although numerical algorithms are available for computing the transform, a “fast” nonlinear Fourier transform that is similarly effective as the fast Fourier transform is for computing the common Fourier transform has not been caution tape jacket
Position and momentum spaces - Wikipedia
WebMar 27, 2024 · Abstract: In recent years, nonlinear Fourier transform (NFT) has been intensely researched as a scheme for communication over the nonlinear optical fiber and characterizing dynamics in nonlinear optical systems. For the accurate computation of b-coefficients on discrete eigenvalues, the bidirectional algorithm has been proposed … WebIn numerical analysis, the split-step ( Fourier) method is a pseudo-spectral numerical method used to solve nonlinear partial differential equations like the nonlinear Schrödinger equation. The name arises for two reasons. WebMathematically, the duality between position and momentum is an example of Pontryagin duality. In particular, if a function is given in position space, f ( r ), then its Fourier transform obtains the function in momentum space, φ ( p ). Conversely, the inverse Fourier transform of a momentum space function is a position space function. caution killers