1926/10/01 by P. A. M. Dirac · 7 citations
Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #Quantum Mechanics and Applications #Quantum chaos and dynamical systems
paper · pdf · doi:10.1098/rspa.1926.0133
openalex publication_date 1926/10/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/25
Abstract The new mechanics of the atom introduced by Heisenberg may be based on the assumption that the variables that describe a dynamical system do not obey the commutative law of multiplication, but satisfy instead certain quantum conditions. One can build up a theory without knowing anything about the dynamical variables except the algebraic laws that they are subject to, and can show that they may be represented by matrices whenever a set of uniformising variables for the dynamical system exists. It may be shown, however (see 3), that there is no set of uniformising variables for a system containing more than one electron, so that the theory cannot progress very far on these lines. A new development of the theory has recently been given by Schrödinger. Starting from the idea that an atomic system cannot be represented by a trajectory, i. e., by a point moving through the co-ordinate space, but must be represented by a wave in this space, Schrödinger obtains from a variation principle a differential equation which the wave function ψ must satisty. This differential equation turns out to be very closely connected with the Hamiltonian equation which specifies the system, namely, if H (qr, Pr - W = 0 is the Hamiltonian equation of the system, where the qr, Pr are canonical variables, then the wave equation for ψ is H(qr, ih ∂/∂q) - W ψ = 0.