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in the articles [8–10]. This correspondence is reached by introducing an effective slit’s half- width 

where double b , a = 2 b , is adopted as a metric width of the slit. Now, let us also define the complex time-dependent spreading [9] 

This spreading consists of real and imaginary parts. The imaginary part, Δ x$_{1}$ = ¯ hτ/ 2 mσ , emergent in Eq (14), represents uncertainty of the particle position on the axis x . What is physical sense of this part? First, we rewrite the imaginary part in the following form m Δ x$_{1}$/τ = ¯ h/ 2 σ . Observe that Δ x$_{1}$/τ is an uncertainty, δv$_{x}$ , of a drift velocity of the particle along the axis x . Consequently, δp$_{x}$ = mδv$_{x}$ is the uncer- tainty of its momentum along the same axis. On the other hand, let the effective slit width 2 σ be uncertainty of the particle coordinate, δx = 2 σ at passing across the slit. As a result, we find δp$_{x}$δx = ¯ h . One can see, it is the Heisenberg uncertainty principle [7]. 

By replacing relevant expressions in Eq. (16) by the parameters (17) and (18) we get the Gaus- sian wave packet in the following form 

Here we have rewritten the square root of imag- inary unit as a factor exp { i 3 π/ 4 } = √ − i . 

Pay attention to Eq. (19), the time parame- ter T did not disappear fully, but it remained in the denominator. In fact, it means, that by removing the particle source to infinity, its inten- sity, ψ $^{†}$ψ , in the vicinity of the slit grating be- come weaker in T − 1 times. We will suppose, that a particle beam from the source is monochro- matic, i.e., velocities of all particles are equal to the same quantity v$_{z}$ . Given path length Z from the source to the slit grating, the velocity is 

<img src='content_image/381318.jpg'>

<img src='content_image/381315.jpg'>

<img src='content_image/381316.jpg'>

v$_{z}$ = Z/T . And the momentum of the particles is p$_{z}$ = mv$_{z}$ , where m is its mass. 

De Broglie relations set momentum p$_{z}$ and en- ergy E = p 2 $_{z}$/ 2 m of the particle in correspon- dence with its wave characteristics such as a wave vector k$_{z}$ = p$_{z}$/ ¯ h and a frequency ω = E/ ¯ h . In that case, a plane wave mentioned earlier can be written down as exp { i ωt − i k$_{z}$z } . Now, the Gaussian wave packet (19) can be supple- mented by this plane wave, that describes, in the paraxial approximation [12], spreading of in- cident wave along the axis z : 

<img src='content_image/381317.jpg'>

Since in the paraxial approximation τ = z/v$_{z}$ , then argument of the wave function contains z instead of τ . In this case, interference experi- 

<img src='content_image/381321.jpg'>

ment can be considered on an N -slit grating sit- uated in a plane ( x, z ), as shown in Fig. 4. 

One can see, by comparing equation (20) with such a formula presented in [10], that with ex- ception of some details these formulas are equiv- alent. For example, presence of the constant phase 3 π/ 4 in Eq. (20) is not critical for further observation of interference effects. Essential dif- ferences are, however, observed in normalization factors. Namely, the term 

<img src='content_image/381320.jpg'>

