Publications related to Solution of Schrödinger equation for a step potential

Coupled-mode theory for stationary and nonstationary resonant sound propagation

Romain Christophe Rémy Fleury, Theodoros Koutserimpas

In this paper, we present a complete analytical derivation of the equations used for stationary and nonstationary wave systems regarding resonant sound transmission and reflection described by the phenomenological coupled-mode theory. We calculate the prop ...

2019

A time-reversible integrator for the time-dependent Schrödinger equation on an adaptive grid

Jiri Vanicek, Seonghoon Choi

One of the most accurate methods for solving the time-dependent Schrödinger equation uses a combination of the dynamic Fourier method with the split-operator algorithm on a tensor-product grid. To reduce the number of required grid points, we let the grid ...

2019

Nonadiabatic effects in electronic and nuclear dynamics

Majed Chergui, Ursula Röthlisberger, Jiri Vanicek, Martin Peter Bircher, Tomas Zimmermann, Elisa Liberatore, Aurélien Kevin Fabrice Patoz, Nicholas John Browning

Due to their very nature, ultrafast phenomena are often accompanied by the occurrence of nonadiabatic effects. From a theoretical perspective, the treatment of nonadiabatic processes makes it necessary to go beyond the (quasi) static picture provided by th ...

2017

Geometric Integrators for Nonadiabatic Molecular Quantum Dynamics Induced by the Interaction with the Electromagnetic Field

Aurélien Kevin Fabrice Patoz

Understanding the elementary steps involved in a chemical reaction forms the cornerstone of physical chemistry research. One way to deepen this understanding is by studying chemical and physical processes using linear and nonlinear spectroscopic techniques ...

EPFL2017

Odd linking and bifurcation in gaps: the weakly indefinite case

In this paper, we consider nonlinear Schrodinger equations of the following type: -Delta u(x) + V (x) u(x) -q(x)|u(x)|sigma u(x) =lambda u(x), x is an element of R-N, u is an element of H-1(R-N) \ {0}, where N >= 2 and sigma > 0. We concentrate on situatio ...

Royal Society of Edinburgh Scotland Foundation, Cambridge2013

Phase Gradient Estimation Techniques in Fringe Analysis

Rajshekhar Gannavarpu

The thesis introduces novel techniques in the field of fringe analysis for direct estimation of phase gradients or derivatives. A pseudo Wigner-Ville distribution based method is proposed to reliably estimate the phase derivatives from a single fringe patt ...

EPFL2012

Accelerating Calculations of Ultrafast Time-Resolved Electronic Spectra with Efficient Quantum Dynamics Methods

Jiri Vanicek, Miroslav Sulc, Marius Wehrle

We explore three specific approaches for speeding up the calculation of quantum time correlation functions needed for time-resolved electronic spectra. The first relies on finding a minimum set of sufficiently accurate electronic surfaces. The second incre ...

2011

Bound states of the Schrödinger-Newton model in low dimensions

Joachim Stubbe, Marc Vuffray

We prove the existence of quasi-stationary symmetric solutions with exactly n >= 0 zeros and uniqueness for n = 0 for the Schrodinger-Newton model in one dimension and in two dimensions along with an angular momentum m >= 0. Our result is based on an analy ...

2010