Semi-classical limit of an inverse problem for the Schrödinger equation

by   Shi Chen, et al.

It is a classical derivation that the Wigner equation, derived from the Schrödinger equation that contains the quantum information, converges to the Liouville equation when the rescaled Planck constant ϵ→0. Since the latter presents the Newton's second law, the process is typically termed the (semi-)classical limit. In this paper, we study the classical limit of an inverse problem for the Schrödinger equation. More specifically, we show that using the initial condition and final state of the Schrödinger equation to reconstruct the potential term, in the classical regime with ϵ→0, becomes using the initial and final state to reconstruct the potential term in the Liouville equation. This formally bridges an inverse problem in quantum mechanics with an inverse problem in classical mechanics.


page 1

page 2

page 3

page 4


Semi-classical limit for the varying-mass Schrödinger equation with random inhomogeneities

The varying-mass Schrödinger equation (VMSE) has been successfully appli...

The Carleman-Newton method to globally reconstruct a source term for nonlinear parabolic equation

We propose to combine the Carleman estimate and the Newton method to sol...

On an inverse problem of nonlinear imaging with fractional damping

This paper considers the attenuated Westervelt equation in pressure form...

About the Stein equation for the generalized inverse Gaussian and Kummer distributions

We propose a Stein characterization of the Kummer distribution on (0, ∞)...

An inverse problem for a semi-linear wave equation: a numerical study

We consider an inverse problem of recovering a potential associated to a...

Information geometry and Frobenius algebra

We show that a Frobenius sturcture is equivalent to a dually flat sturct...

Please sign up or login with your details

Forgot password? Click here to reset