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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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