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BARRIER PENETRATION: SEMI-CLASSICAL APPROXIMATION

Jean Zinn-Justin

in Path Integrals in Quantum Mechanics

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198566748
eISBN:
9780191717994
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566748.003.0008
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

A classical particle is always reflected by a potential barrier if its energy is lower than the potential. In contrast, a quantum particle has a non-vanishing probability to tunnel through a barrier, ... More


Transport equations for the one-body density

Helmut Hofmann

in The Physics of Warm Nuclei: with Analogies to Mesoscopic Systems

Published in print:
2008
Published Online:
September 2008
ISBN:
9780198504016
eISBN:
9780191708480
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198504016.003.0021
Subject:
Physics, Nuclear and Plasma Physics

This chapter begins by calculating the Wigner transform for the von Neumann equation for the one-body density operator. It shows how the Liouville equation follows in leading order in an expansion to ... More


QUANTUM EVOLUTION AND SCATTERING MATRIX

Jean Zinn-Justin

in Path Integrals in Quantum Mechanics

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198566748
eISBN:
9780191717994
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566748.003.0009
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

This chapter shows how scattering problems are formulated in the framework of path integrals. In quantum mechanics, the state of an isolated system evolves under the action of a unitary operator, as ... More


Overview

C. Julian Chen

in Introduction to Scanning Tunneling Microscopy: Second Edition

Published in print:
2007
Published Online:
September 2007
ISBN:
9780199211500
eISBN:
9780191705991
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199211500.003.0001
Subject:
Physics, Condensed Matter Physics / Materials

This chapter presents the basic designs and working principles of STM and AFM, as well as an elementary theory of tunneling and the imaging mechanism of atomic resolution. Three elementary theories ... More


Euclidean path integrals and quantum mechanics (QM)

Jean Zinn-Justin

in Quantum Field Theory and Critical Phenomena: Fifth Edition

Published in print:
2021
Published Online:
June 2021
ISBN:
9780198834625
eISBN:
9780191872723
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198834625.003.0002
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Functional integrals are basic tools to study first quantum mechanics (QM), and quantum field theory (QFT). The path integral formulation of QM is well suited to the study of systems with an ... More


Path Integral Formulation of Quantum Mechanics

Xiao-Gang Wen

in Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an Origin of Light and Electrons

Published in print:
2007
Published Online:
February 2010
ISBN:
9780199227259
eISBN:
9780191713019
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199227259.003.02
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter introduces path integral and various correlation functions at zero and non-zero temperatures to study interacting quantum systems. Semi-classical approximation and instanton effects are ... More


Quantum transport

B. K. Ridley FRS

in Quantum Processes in Semiconductors

Published in print:
2013
Published Online:
December 2013
ISBN:
9780199677214
eISBN:
9780191760624
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199677214.003.0011
Subject:
Physics, Condensed Matter Physics / Materials

In certain cases, the electron involved in the scattering process may begin in a well-defined initial state and end up in an equally well-defined final state. Scattering is assumed to conserve energy ... More


Overview

C. Julian Chen

in Introduction to Scanning Tunneling Microscopy

Published in print:
2021
Published Online:
April 2021
ISBN:
9780198856559
eISBN:
9780191889905
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198856559.003.0001
Subject:
Physics, Condensed Matter Physics / Materials

This chapter presents the basic designs and working principles of STM and AFM, as well as an elementary theory of tunneling and the imaging mechanism of atomic resolution. Three elementary theories ... More


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