Stability after confinement of the H atom

Information and quantum theories: an analysis in one-dimensional systems

“…To integrate in new interval is the same as multiply the S x for fundamental state by n. However, the factor 1/n keeps the integral values for excited states the same as for fundamental one. For sine solutions (17), an identical answer is obtained since sine and cosine functions are equal by a π/2 phase shift. A qualitative explanation about behavior of modified entropies for different states can be obtained by analysis of the probability densities in position and momentum spaces.…”

“…To integrate in the new interval is the same as multiplying the S x for the fundamental state by n. However, the factor 1/n keeps the integral values for excited states the same as for the fundamental one. For sine solutions (17), an identical answer is obtained since sine and cosine functions are equal by a π/2 phase shift.…”

“…A mathematical explanation is given by normalization constants. Normalization constants for probability density ρ(x) are the same for different states, depends only on x c −1 for different wave functions in equations (16) and (17). In this way, the integrand of equation (3) for different states are related by a scaling factor equal n to same confinement distance.…”

“…We investigated the particle confined in a box in the ground (n = 1) and also in the two first excited (n = 2 and 3) states by equations ( 16)and (17). The values of modified information entropies S x and S p for some values of x c are given in table 2 and displayed in figure 6.…”

“…Initially identified as an autonomous area, the mathematical theory of communication or information theory now has its fundamental concepts utilized in distinct fields of expertise, mainly through the informational entropy [9][10][11]. Information theory in the atomic, molecular and chemical physics context has generated a reasonable number of analyses [12][13][14][15][16][17][18][19]. Works about ions in plasma environments [20] and correlation measurements [21,22] show great results in favor of the informational treatment.…”