scholarly journals A fundamental solution to the Schrödinger equation with Doss potentials and its smoothness

2017 ◽  
Vol 58 (5) ◽  
pp. 053506 ◽  
Author(s):  
Martin Grothaus ◽  
Felix Riemann
Keyword(s):  
Fundamental Solution ◽  
Schrödinger Equation ◽  
Schrodinger Equation

On a complex fundamental solution of the Schrödinger equation

2017 ◽  
Vol 95 (2) ◽  
pp. 122-124
Author(s):  
A. G. Chechkin ◽  
A. S. Shamaev
Keyword(s):  
Fundamental Solution ◽  
Schrödinger Equation ◽  
Schrodinger Equation

ON THE BEHAVIOR AT INFINITY OF THE FUNDAMENTAL SOLUTION OF TIME DEPENDENT SCHRÖDINGER EQUATION

2001 ◽  
Vol 13 (07) ◽  
pp. 891-920 ◽  
Author(s):  
KENJI YAJIMA
Keyword(s):  
Asymptotic Behavior ◽  
Integral Operator ◽  
Fundamental Solution ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Schrodinger Equation ◽  
Fourier Integral Operator ◽  
Fourier Integral ◽  
Time Dependent ◽  
Initial Value

We show that the asymptotic behavior at infinity of the fundamental solution of the initial value problem for the free Schrödinger equation or of the harmonic oscillator at non-resonant time is stable under subquadratic perturbations. We also show that the same is true for the phase and the amplitude of the Fourier integral operator representing the propagator.

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