Lower Bounds to Eigenvalues of the Schrödinger Equation. III. On the Relationship between the Method of Intermediate Hamiltonians and the Partitioning Technique

1967 ◽  
Vol 47 (11) ◽  
pp. 4706-4713 ◽  
Author(s):  
Timothy M. Wilson
Keyword(s):  
Schrödinger Equation ◽  
Lower Bounds ◽  
Schrodinger Equation ◽  
The Relationship ◽  
Partitioning Technique ◽  
Intermediate Hamiltonians

Upper and lower bounds for the Schrödinger-equation eigenvalues

1986 ◽  
Vol 116 (9) ◽  
pp. 407-409 ◽  
Author(s):  
F.M. Fernandez ◽  
J.F. Ogilvie ◽  
R.H. Tipping
Keyword(s):  
Schrödinger Equation ◽  
Lower Bounds ◽  
Schrodinger Equation ◽  
Upper And Lower Bounds

scholarly journals On PT Symmetry Systems: Invariance, Conservation Laws, and Reductions

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
P. Masemola ◽  
A. H. Kara
Keyword(s):  
Schrödinger Equation ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Schrodinger Equation ◽  
Lie Symmetries ◽  
Pt Symmetry ◽  
Noether Symmetries ◽  
Cubic Schrödinger Equation ◽  
The Relationship

An analysis of a PT symmetric coupler with “gain in one waveguide and loss in another” is made; a transformation in the PT system and some assumptions results in a scalar cubic Schrödinger equation. We investigate the relationship between the conservation laws and Lie symmetries and investigate a Lagrangian, corresponding Noether symmetries, conserved vectors, and exact solutions via “double reductions.”

scholarly journals Sharp blowup rate for NLS with a repulsive harmonic potential

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Rui Zhou
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Lower Bounds ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Harmonic Potential ◽  
Upper And Lower Bounds ◽  
Singular Solutions ◽  
Blowup Rate ◽  
Nonlinear Schrödinger

AbstractIn this paper, we are concerned with the blowup solutions of the $L^{2}$ L 2 critical nonlinear Schrödinger equation with a repulsive harmonic potential. By using the results recently obtained by Merle and Raphaël and by Carles’ transform we establish in a quite elementary way universal and sharp upper and lower bounds of the blowup rate for the blowup solutions of the aforementioned equation. As an application, we derive upper and lower bounds on the $L^{r}$ L r -norms of the singular solutions.

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