2013/06/07 by Boháčik, J., Prešnajder, P., P. August'in +1
Engineering · Mathematics · Physics and Astronomy · #Acoustic Wave Phenomena Research #Advanced Electrical Measurement Techniques #Anharmonicity #Exponent #FOS: Physical sciences #Harmonic #Harmonic oscillator #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Mathematical analysis #Mathematical physics #Mathematics #Perturbation (astronomy) #Perturbation theory (quantum mechanics) #Physics #Propagator #Quantum Physics (quant-ph) #Quantum mechanics #Scientific Research and Discoveries #Series (stratigraphy) #Term (time)
paper · pdf · doi:10.48550/arxiv.1306.1694
openalex publication_date 2013/06/07 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
We find the possibility of the non-perturbative an-harmonic correction to Mehler's formula for propagator of the harmonic oscillator. We evaluate the conditional Wiener measure functional integral with a term of the fourth order in the exponent by an alternative method as in the conventional perturbative approach. In contrast to the conventional perturbation theory, we expand into power series the term linear in the integration variable in the exponent. We discuss the case, when the starting point of the propagator is zero. We present the results in analytical form for positive and negative frequency.