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Functional Integration pp 175–189Cite as

Dependence of the Feynman Path Integral on Discretization the Case of a Spinless Particle in an External Electromagnetic Field

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Abstract

The transition amplitude (t,x;s,y) i.e. the probability amplitude for finding a particle at the point XεR3, at the time instant t, when it is known that at the time s<t the particle was at yεR3, satisfies the conditions

$$\begin{array}{*{20}{c}} {\left( {i{\text{ }}\hbar {\partial _t} - \hat H} \right)\left( {t,x;s,y} \right) = 0} \\ {\lim \left( {t,x;s,y} \right) = \delta \left( {x - y} \right).} \end{array}$$
(1)

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References

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Author information

Authors and Affiliations

  1. Institute of Theoretical Physics, University of Wrocław, Poland

    Włodzimierz Garczynski

Authors
  1. Włodzimierz Garczynski
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Editor information

Editors and Affiliations

  1. Institut de Physique Théorique, Université Catholique de Louvain, Louvain-la-Neuve, Belgium

    Jean-Pierre Antoine  & Enrique Tirapegui  & 

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© 1980 Plenum Press, New York

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Garczynski, W. (1980). Dependence of the Feynman Path Integral on Discretization the Case of a Spinless Particle in an External Electromagnetic Field. In: Antoine, JP., Tirapegui, E. (eds) Functional Integration. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-7035-6_13

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  • DOI: https://doi.org/10.1007/978-1-4615-7035-6_13

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4615-7037-0

  • Online ISBN: 978-1-4615-7035-6

  • eBook Packages: Springer Book Archive

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