5 wise as before but with a new distribution center x$_{1}$ be shifted on a value Δ x from the point x$_{0}$ . Width b$_{1}$ of the new distribution is also broad- ened. The both parameters, x$_{1}$ and b$_{1}$ , are de- termined by expressions a ray within an angle of beam α . Observe, how- ever, that quantum particles, in contrast to the classical ones, at scattering on the slit manifest wavelike nature. Relation between matter waves and their wavelengths had been established by de Broglie. Observe, that the wavelike nature underlies phase shifts of the moving particles in an observation point. as shown in Fig. 3. One can see, all classical tra- jectories, passing through the Gaussian slit, form Taking into account the above stated, Eq. (10) can be rewritten in the following form By substituting G ( ξ ) from Eq. (11) to this expression and integrating it we obtain Here Δ x has been replaced by its explicit expression Δ x = ( x$_{1}$ − x$_{0}$ ). Rewrite Eq. (14) by executing insignificant transformations The transformation, resulting to Eq. (15), affects only arrangement of the time parameters τ and T . Now, according to Eq. (12) we could intro- duce b$_{1}$ = b (1 + τ/T ). But in the limit T → ∞ we have equality b$_{1}$ = b . So, we can remove ev- erywhere in Eq (15) the term (1 + τ/T ). Due to the limit T → ∞ we have put source of the par- ticles to infinity. According to this trick, we can now suppose that the particles incident to the slit grating are described by wave function that is a plane wave. In accordance with the limit T → ∞ , Eq. (15) transforms to the following form Let us clarify correspondence of this formula with the Gaussian wave packet, that is described ψ ( x$_{1}$, x$_{0}$ ) = √ m 2 π i ¯ hT$^{(}$ 1 + i ¯ hτ mb 2 $_{)}$− 1 / 2 × exp$^{{}$ − ( x$_{1}$ − x$_{0}$ ) $^{2}$/ 2 b 2 1 + i ¯ hτ/mb 2 } . (16) ψ ( x$_{1}$, x$_{0}$ ) = √ m 2 π i ¯ h$^{[}$ T (1 + τ/T )$^{(}$1 + i ¯ hτ mb $^{2}$(1 + τ/T )$^{$_{)]}$−}$$^{1}$$^{/}$$^{2}$ × exp$^{{}$ i m 2¯ h$^{(}$ ( x$_{1}$ − x$_{0}$ ) 2 τ + x 2 0 T − ( − ( x$_{1}$ − x$_{0}$ ) /τ + x$_{0}$/T ) $^{2}$τ (1 + τ/T )(1 + i ¯ hτ/mb $^{2}$(1 + τ/T )) .$^{}}$ (15) ψ ( x$_{1}$, x$_{0}$ ) = √ m 2 π i ¯ h$^{[}$ T τ$^{(}$ 1 T + 1 τ + i ¯ h mb 2 $_{)]}$− 1 / 2 × exp$^{{}$ i m 2¯ h$^{((}$ ( x$_{1}$ − x$_{0}$ ) 2 τ + x 2 0 T ) − ( − ( x$_{1}$ − x$_{0}$ ) /τ + x$_{0}$/T ) 2 (1 /τ + 1 /T + i ¯ h/mb $^{2}$) )} . (14) ψ ( x$_{1}$, x$_{0}$ ) = ∞ ∫ −∞ mG ( ξ ) 2 π i ¯ h √ T τ$^{(}$ exp$^{{}$ i m 2¯ h$^{[}$ (Δ x − ξ ) 2 τ + ( x$_{0}$ − ξ ) 2 T ]}) dξ. (13) x$_{1}$ = x$_{0}$$^{(}$ 1 + τ T$^{)}$ , b$_{1}$ = b$^{(}$ 1 + τ T$^{)}$ , (12) A. Solitary Gaussian slit