The State That Is Not a State: Gamow's Outgoing Wave and the Manufactured Lifetime

In 1928 George Gamow explained alpha decay by quantum tunnelling: a particle pre-formed inside the nucleus leaks through its barrier, and the lifetime is the assault frequency times the barrier's penetration factor. The factor is derived in the paper and is one of the permanent returns of twentieth-century physics. The object the lifetime is read off, however, is a "decaying state" obtained by solving the stationary Schrödinger equation under a boundary condition imposed by hand — purely outgoing waves at infinity — which returns a complex eigenvalue E - iΓ/2 and an eigenfunction that grows exponentially outside the barrier and belongs to no Hilbert space. This paper runs one declared Hamiltonian three ways. Under the outgoing-wave-only (Siegert) condition it has a pole at E_R = 2.253744 with width Γ = 0.176964 and lifetime τ = 5.650874. A real-energy resonance scan of the same barrier — no complex eigenvalue anywhere — finds the same resonance with width 0.178767, differing from the pole's by a relative +0.010189. Boxed by a second wall, the same Hamiltonian is self-adjoint, its spectrum is real, and every width is 0.000000 exactly: nothing decays. The lifetime is manufactured by the boundary condition; the price of the postulate is the whole of Γ. Count: 1 boundary-condition postulate, 0 derivations in 1928 of the decaying state as an eigenstate of a self-adjoint problem. Census headline, unchanged: NOT SOLVED / PARTIAL · producing-count 0.