scholarly journals The Talbot effect as the fundamental solution to the free Schrödinger equation

2021 ◽  
Vol 78 (2) ◽  
pp. 233-253
Author(s):  
Daniel Eceizabarrena
Keyword(s):  
Fundamental Solution ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Talbot Effect

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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