Quantum revival

In quantum mechanics, the quantum revival is a periodic recurrence of the quantum wave functionfrom its original form during the time evolution either many times in space as the multiple scaled fractionsin the form of the initial wave function (fractional revival) or approximately or exactly to its original form from the beginning (full revival). The quantum wave function periodic in time exhibits therefore the full revival every period. The phenomenon of revivals is most readily observable for the wave functions being well localized wave packets at the beginning of the time evolution for example in the hydrogen atom. For Hydrogen the fractional revivals show up as multiple angular Gaussian bumps around the circle drawn by the radial maximum of leading circular state component (that with the highest amplitude in the eigenstate expansion) of theoriginal localized state and the full revival as the original Gaussian.The full revivals are exact for the infinite quantum well, harmonic oscillator or the hydrogen atom, while for shorter times are approximate for the hydrogen atom and a lot of quantum systems. In quantum mechanics, the quantum revival is a periodic recurrence of the quantum wave functionfrom its original form during the time evolution either many times in space as the multiple scaled fractionsin the form of the initial wave function (fractional revival) or approximately or exactly to its original form from the beginning (full revival). The quantum wave function periodic in time exhibits therefore the full revival every period. The phenomenon of revivals is most readily observable for the wave functions being well localized wave packets at the beginning of the time evolution for example in the hydrogen atom. For Hydrogen the fractional revivals show up as multiple angular Gaussian bumps around the circle drawn by the radial maximum of leading circular state component (that with the highest amplitude in the eigenstate expansion) of theoriginal localized state and the full revival as the original Gaussian.The full revivals are exact for the infinite quantum well, harmonic oscillator or the hydrogen atom, while for shorter times are approximate for the hydrogen atom and a lot of quantum systems. The plot of collapses and revivals of quantum oscillations of the JCM atomic inversion. Consider a quantum system with the energies E i {displaystyle E_{i}} and the eigenstates ψ i {displaystyle psi _{i}} and let the energies be the rational fractions of some constant C {displaystyle C} (for example for hydrogen atom M i = 1 {displaystyle M_{i}=1} , N i = i 2 {displaystyle N_{i}=i^{2}} , C = − 13.6 e V {displaystyle C=-13.6eV} . Then the truncated (till N m a x {displaystyle mathbb {N} _{max}} of states) solution of the time dependent Schrödinger equation is