Abstract
We study the time-dependent Schrodinger equation with nite number of Dirac \delta and\delta' potentials with time dependent strengths in one dimension. We obtain the formal solution for generic timedependent strengths and then we study the particular cases for single delta potential and limiting cases for finitely many delta potentials. Finally, we investigate the solution of time dependent Schrodinger equation for \delta' potential with particular forms of the strengths.
Highlights
Dirac delta potentials in quantum mechanics have been used to model different physical systems almost since the beginning of quantum mechanics
The paper is organized as follows: In section 2, we obtain a formal expression of the propagator for a finite number of Dirac δ potentials with time dependent strengths and solve the time dependent Schrödinger equation for this system
We have obtained a formal expression of the propagator for finite number of Dirac δ potentials with time dependent strengths and solved the time dependent Schrödinger equation for this system
Summary
Dirac delta potentials in quantum mechanics have been used to model different physical systems almost since the beginning of quantum mechanics. Time dependent one dimensional point interactions have been studied in Campbell [36] and the exact solution to the initial value problem for Schrödinger equation has been given for some particular form of strength λ(t) of the Dirac delta potential. The system has been investigated in Hmidi et al [37] more rigorously and the regularity assumptions on λ(t) is determined for which the initial value problem defines a unitary strongly continuous dynamical system on L2(R) Such time-dependent point interactions have been studied rigorously in order to model asymptotic complete ionization and suitable conditions on the function λ(t) has been determined for ionization problem [38,39,40,41].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
