Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Theoretical and Mathematical Physics

Green's functions of the Schrödinger equation for the simplest systems

V. L. Bakhrakh, S. I. Vetchinkin

Published Mar 1, 1971• 32 citations
Publisher
DOI
10.1007/bf01030109

Related papers

Green’s Functions of the Single-Particle Schrödinger Equation

John C. Inkson

Springer eBooks•Jan 1, 1984•0 citations

A new method for calculation of the green functions of the Schrödinger equation

Alexander I. Milstein

Physics Letters A•May 1, 1987•0 citations

The green's functions of the Schrödinger equation for the simplest systems

S. I. Vetchinkin, V. L. Bachrach

Abstract The Green's functions for the simplest quantum mechanical systems the linear harmonic oscillator, the three‐dimensional isotropic oscillator, the Morse oscillator, the Kratcer potential, and the double‐minimum potential V(x) = (mw2/2)(/x/−R)2 are presented in closed analytical forms.

International Journal of Quantum Chemistry•Jan 1, 1972•12 citations

Schrödinger Equation for One-Dimensional Systems

Luigi E. Picasso

UNITEXT for physics•Oct 26, 2015•0 citations

The Green function for simplest quantum graphs

K.K. Sabirov, U. A. Aminov, Kh.Sh. Saparov +2 more

We treat the problem of the Green function for quantum graphs by focusing on such topologies as star and tree graphs.The exact Green function for the Schrödinger equation on primary star graphs is derived in the form of 3 × 3-matrix using the vertex boundary conditions providing continuity and current conservation.Extension of the approach for the derivation for the Green function on tree graph is presented.Possible practical applications of the obtained results are discussed.

Nanosystems Physics Chemistry Mathematics•Dec 21, 2015•1 citation

The Free Particle. The Time-Dependent Schrödinger Equation

Ana Marı́a Cetto, Luis de la Peña

Chapter 7 is devoted to the free particle and the derivation of the time-dependent Schrödinger equation. The free particle might be thought to be the simplest quantum problem of all, but a detailed treatment of it, including both Born and Dirac normalization, serves to highlight some surprising features. Powerful tools are introduced that are of wider application, notably the Green function method and the Feynman propagator. This material paves the way for the study of the time-dependent Schrödinger equation, the introduction of the current density of particles and the distinction between pure states and mixtures; the equation is applied specifically to the study of coherent states. The chapter ends with an introduction to the propagator in the general case.

Cambridge University Press eBooks•Dec 18, 2025•0 citations
Chapter 7 is devoted to the free particle and the derivation of the time-dependent Schrödinger equation. The free particle might be thought to be the simplest quantum problem of all, but a detailed treatment of it, including both Born and Dirac normalization, serves to highlight some surprising features. Powerful tools are introduced that are of wider application, notably the Green function method and the Feynman propagator. This material paves the way for the study of the time-dependent Schrödinger equation, the introduction of the current density of particles and the distinction between pure states and mixtures; the equation is applied specifically to the study of coherent states. The chapter ends with an introduction to the propagator in the general case.