1928/01/01 by J. Robert Oppenheimer · 5 citations
Mathematics · Physics and Astronomy · #Spectral Theory in Mathematical Physics #Quantum chaos and dynamical systems #Quantum Mechanics and Non-Hermitian Physics #Physics #Eigenfunction #Mathematical physics #Quantum mechanics #Lambda #Atomic physics
paper · doi:10.1103/physrev.31.66
openalex publication_date 1928/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
In Section 1 it is shown that the normalization of the characteristic functions corresponding to a continuous spectrum, which has been introduced by Hellinger and Weyl, satisfies the requirements of the \ensuremathδ-normalization of the Dirac-Jordan transformation theory. It is further shown that this normalization makes the flux to and from infinity of systems for which an integral of motion \ensuremathβ lies in the little range \ensuremathΔ\ensuremathβ^\ensuremath' equal to (\frac\ensuremath∂Eh\ensuremath∂\ensuremathβ^\ensuremath')\ensuremathΔ\ensuremathβ^\ensuremath'.In Section 2 the condition for the validity of classical mechanics in the form grad \ensuremathλ\ensuremath≪1, where \ensuremathλ is the instantaneous wave length \ensuremathλ=(\frach2\ensuremathπ)[2M(E\ensuremath-U)]^\ensuremath-(1)/(2), is applied to establish Rutherford's formula for the scattering of \ensuremathα-particles.In Section 3 a method is developed for computing the transition probabilities between states of the same energy, and which are represented by almost orthogonal eigenfunctions. The theory is applied to the ionization of hydrogen atoms in a constant electric field. The period of ionization in a field of 1 volt per cm is 10^1010 sec. The bearing of such transitions on the problem of metallic conduction is discussed.