The Heitler equation of the hydrogen atom has been adapted to its nucleus where the centrifugal force is replaced by the magnetic repulsive force, solved graphically, by trial and error, without fit to experiment. As by chance, one obtains, at the lowest horizontal inflection point, with a ...
elementforSchr¨odingerequation WANGPingli 1 ,SHIDongyang 2 (1.SchoolofMathematicsandStatistics,XuchangUniversity,Xuchang461000,Henan,China; 2.SchoolofMathematicsandStatistics,ZhengzhouUniversity,Zhengzhou450001,Henan,China) Abstract:ThebilinearfiniteelementapproximationismainlydiscussedforSchr¨odingerequation.Thesu...
R. Weder, Scattering for the forced non-linear Schr¨odinger equation with a potential on the half-line, preprint, 2002.Ricardo Weder, The forced non-linear Schrodinger equation with a potential on the half-line, Math. Methods Appl. Sci. 28 (10) (2005) 1237-1255....
dinger equation i1 + 1 + 2(|1 |2 + |2 |2 )1 = 0, i2 + 2 + 2(|1 |2 + |2 |2 )2 = 0. (1a) (1b) (2a) 2 0 )]Φ , (2b) The integrability of this system was proved by Manakov, which is here named as the integrable Manakov[6] system. Recently, the rogue ...
The Schrdinger equation is one of the most important equations in mathematics, physics and also engineering. We outline some connections between transformations of non-linear equations, the Schrdinger equation and the inverse scattering transform. After some remarks on generalizations into higher ...
A Schrödinger-like equation for a single free quantum particle is presented. It is argued that this equation can be considered a natural relativistic extension of the Schrödinger equation for energies smaller than the energy associated to the particle's mass. Some basic properties of this ...
The nonlocal nonlinear Schr?dinger equation(NNLSE)with competing weakly nonlocal nonlinearity and parabolic law nonlinearity is explored in the current work.A powerful integration tool,which is a modified form of the simple equation method,is used to construct the dark and singular 1-soliton ...
We prove Strichartz estimates with fractional loss of derivatives for the Schrödinger equation on any Riemannian compact manifold. As a consequence we infer low regularity local well-posedness results in any dimension, as well as global existence results for the Cauchy problem of nonlinear ...
doi:10.1002/0471221600.ch7Schrödinger equationtime‐dependent statefinite‐difference analysistime‐independent statefinite‐element analysisKawano, KenjiAnritsu CorporationKitoh, TsutomuNippon Telegraph and Telephone CorporationJohn Wiley & Sons, Inc.
Schrödinger equationquantum‐mechanical harmonic oscillatorenergypotential energyEuler's formuladoi:10.1002/9783527618934.ch15WangFrank Y.Wiley‐VCH Verlag GmbH