## ABSTRACT

The Euclidean theory can be formally defined as the theory which is obtained from the ordinary (pseudo-Euclidean) theory by the substitution t → −it. This substitution transforms the operator K in Eq. (1.2) into the Euclidean operator K
_{e}, and the quantum Schrödinger equation becomes an equation of the heat-conduction type: i∂_{
t
}ψ = Hψ → −∂_{
t
}ψ = Hψ (it is assumed that H does not depend explicitly on time).