• DOI:10.1098/RSPA.1926.0133
• Corpus ID: 122757433

On the Theory of quantum mechanics

@article{DiracOnTT,
  title={On the Theory of quantum mechanics},
  author={Paul Adrien Maurice Dirac},
  journal={Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences},
  volume={112},
  pages={661-677}
}

• P. Dirac
• Published 1 October 1926
• Mathematics
• Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences

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 Schrodinger. 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, Schrodinger 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 ( q r , P r - W = 0 is the Hamiltonian equation of the system, where the q r , P r are canonical variables, then the wave equation for ψ is {H( q r , ih ∂/∂ q ) - W} ψ = 0.