Abstract
We study the connection between the phase and the amplitude of the wave function and the conditions under which this relationship exists. For this we use the model of particle in a box. We have shown that the amplitude can be calculated from the phase and vice versa if the log analytical uncertainty relations are satisfied.
Highlights
In classical physics position and momentum are two conjugate variables that determine motion
If proper analytical conditions are met the phase and amplitude are related by the temporal Kramers–Kronig relations, which are reminiscent in form with the relations obtained by Kramers and Kronig for the real and imaginary parts of the dielectric function [25]
Following Yahalom and Englman [21] who found the existence of a reciprocal relationship between the phase and amplitude of a wave function returned from an infinite potential barrier
Summary
In classical physics position and momentum are two conjugate variables that determine motion. In some cases the presence of more than one component in the state function is a topological effect This determination is based on Longuet–Higgins’ theorem “Topological Test for a Intersections” [20], which states that if a given wave function of an electronic state changes sign when it moves around a loop in a nuclear configuration space, the state must be degenerate with another state at some point in a loop. This allows for the removal of possible ambiguities that arise in the solution at a singular point that can be infinite In addition to this it can often be useful to refer to a number of physical parameters that appear in theory as a complex quantity and that the wave function will include analytical values in relation to them. We remark that the boundary conditions in a Entropy 2022, 24, 312 well are different, than the boundary conditions in the case of an infinite barrier described in [21]
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