Non-Perturbative Anharmonic Correction to Mehler’s Presentation of the Harmonic Oscillator Propagator

Authors

  • J. Boh´acik Institute of Physics, Slovak Academy of Sciences
  • P. August´in Department of Theoretical Physics and Physics Education, Faculty of Mathematics, Physics and Informatics, Comenius University
  • P. Presnajder Department of Theoretical Physics and Physics Education, Faculty of Mathematics, Physics and Informatics, Comenius University

DOI:

https://doi.org/10.15407/ujpe59.02.0179

Keywords:

Non-perturbative anharmonic correction, Mehler’s formula, harmonic oscillator

Abstract

We find the possibility of a non-perturbative anharmonic correction to Mehler’s formula for the propagator of a harmonic oscillator. The conditional Wiener measure functional integral with a fourth-order term in the exponent is evaluated using a method alternative to the conventional perturbative approach. In contrast to the conventional perturbation theory, we expand the term linear in the integration variable in the exponent into a power series. The case where the
starting point of the propagator is zero is discussed. The results are presented in analytical form for positive and negative frequencies.

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Published

2018-10-18

How to Cite

Boh´acik, J., August´in, P., & Presnajder, P. (2018). Non-Perturbative Anharmonic Correction to Mehler’s Presentation of the Harmonic Oscillator Propagator. Ukrainian Journal of Physics, 59(2), 179. https://doi.org/10.15407/ujpe59.02.0179

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Section

General problems of theoretical physics