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We find the possibility of the non-perturbative an-harmonic correction toMehler's formula for propagator of the harmonic oscillator. We evaluate theconditional Wiener measure functional integral with a term of the fourth orderin the exponent by an alternative method as in the conventional perturbativeapproach. In contrast to the conventional perturbation theory, we expand intopower series the term linear in the integration variable in the exponent. Wediscuss the case, when the starting point of the propagator is zero. We presentthe results in analytical form for positive and negative frequency.

The possibility of the non-perturbative an-harmonic correction to Mehler's formula for propagator of the harmonic oscillator