Lower bounds to ground state eigenvalues of the Schr�dinger equation via optimized inner projection: Application to quartic and sextic anharmonic oscillators

1986 ◽  
Vol 30 (S20) ◽  
pp. 65-72 ◽  
Author(s):  
J. ?�?ek ◽  
E. R. Vrscay
Keyword(s):  
Lower Bounds ◽  
Ground State ◽  
Anharmonic Oscillators ◽  
Dinger Equation

scholarly journals Instability of Traveling Pulses in Nonlinear Diffusion-Type Problems and Method to Obtain Bottom-Part Spectrum of Shrödinger Equation with Complicated Potential

2021 ◽  
Author(s):  
Michael I. Tribelsky
Keyword(s):  
Ground State ◽  
Nonlinear Diffusion ◽  
Diffusion Equations ◽  
Nonlinear Diffusion Equations ◽  
Dinger Equation ◽  
Bottom Part ◽  
Diffusion Type ◽  
Traveling Pulses ◽  
General Method ◽  
Diffusion Problems

The instability of traveling pulses in nonlinear diffusion problems is inspected on the example of Gunn domains in semiconductors. Mathematically the problem is reduced to the calculation of the "energy" of the ground state in Schrödinger equation with a complicated potential. A general method to obtain the bottom-part spectrum of such equations based on the approximation of the potential by square wells is proposed and applied. Possible generalization of the approach to other types of nonlinear diffusion equations is discussed.

L 2-exponential lower bounds to solutions of the Schr�dinger equation

1982 ◽  
Vol 87 (2) ◽  
pp. 265-286 ◽  
Author(s):  
Richard Froese ◽  
Ira Herbst ◽  
Maria Hoffmann-Ostenhof ◽  
Thomas Hoffmann-Ostenhof
Keyword(s):  
Lower Bounds ◽  
Dinger Equation
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