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Applied Computational Physics$
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Joseph F. Boudreau and Eric. S. Swanson

Print publication date: 2017

Print ISBN-13: 9780198708636

Published to Oxford Scholarship Online: February 2018

DOI: 10.1093/oso/9780198708636.001.0001

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Quantum mechanics I–few body systems

Quantum mechanics I–few body systems

(p.732) 21 Quantum mechanics I–few body systems
Applied Computational Physics

Joseph F. Boudreau

Eric S. Swanson

Oxford University Press

Several techniques for obtaining the eigenspectrum and scattering properties of one- and two-body quantum systems are presented. More unusual topics, such as solving the Schrödinger equation in momentum space or implementing relativistic kinematics, are also addressed. A novel quantum Monte Carlo technique that leverages the similarity between path integrals and random walks is developed. An exploration of the method for simple problems is followed by a survey of methods to obtain ground state matrix elements. A review of scattering theory follows. The momentum space T-matrix formalism for scattering is introduced and an efficient numerical method for solving the relevant equations is presented. Finally, the method is extended to the coupled channel scattering problem.

Keywords:   bound states, Schrödinger equation, quantum Monte Carlo, scattering, T-matrix, coupled channel scattering

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