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Current issue   Ukr. J. Phys. 2014, Vol. 59, N 2, p.179-192


Boháčik J.1, Augustín P.2, Prešnajder P.2

1 Institute of Physics, Slovak Academy of Sciences
(D´ubravsk´a cesta 9, 845 11 Bratislava, Slovakia; e-mail: bohacik@savba.sk)
2 Department of Theoretical Physics and Physics Education,
Faculty of Mathematics, Physics and Informatics, Comenius University
(Mlynsk´a dolina F2, 842 48 Bratislava, Slovakia; e-mail: peto1506@gmail.com, presnajder@fmph.uniba.sk)

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

Section: General problems of theoretical physics
Original Author's Text: English

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.

Key words: Non-perturbative anharmonic correction, Mehler’s formula, harmonic oscillator.