Revival Physics
In infinite well: Eₙ = n²·E₁
ψ(x,t) = Σₙ cₙ φₙ(x) e^{-iEₙt/ℏ}
Revival time:
T_rev = 2πℏ/(E₁·α)
where α = d²E/dn² × n₀
At t = T_rev/p: p fractional revivals appear — ghost copies of original packet.
1/2 revival: two half-packets
1/3 revival: three copies
Discovered in Rydberg atoms (1990s). Applications in quantum control.