253rd RQC Seminar

• 講演者

  Prof. Jean-Jacques Slotine
  ( MIT )

• 日程

  2026年1月22日(木), 15:30 - 16:30 (3:30pm - 4:30pm)

• 開催場所

  ハイブリッド（Zoom,
  Seminar Room 345-347, 3F, Main Research Building, Wako Campus / 和光地区 研究本館3階 セミナー室 345-347 (C01))

• 講演タイトル

  On Computing Quantum Waves Exactly from Classical Action

• お問合せ

  takahiro.mitani[at]riken.jp

講演概要
We show that the Schr\"odinger equation can be solved exactly based only on classical least action. Fundamental postulates of quantum mechanics can in turn be derived directly from this construction. The results extend to the relativistic Klein-Gordon, Pauli, and Dirac equations, and suggest a smooth transition between physics across scales.

Most quantum mechanics problems have classical versions which involve multiple least action solutions. The associated classical multipaths stem either from the initial position or momentum distribution, or from branch points, generated, e.g., by a multiply connected manifold (double slit experiment), by spatial inequality constraints (particle in a box), or by a singularity (Coulomb potential). We show that the exact Schr\"odinger wave function $\psi$ can be constructed by combining this classical multi-valued action $\phi$ with the classical density $\rho$, which can be easily and analytically computed from $\phi$ along each extremal action path. The construction is general and does not involve any semi-classical approximation.

Examples illustrate how the quantum wave functions for the double-slit and Aharonov-Bohm experiments, quantum tunneling, or the hydrogen atom can be computed exactly from their classical least action counterparts.

These results also provide a simpler computational alternative to Feynman path integrals, as they use only a discrete set of classical paths and avoid zig-zag paths and time-slicing altogether.

Work in progress explores more ontological questions. From this perspective, quantum wave collapse at measurement can be derived from the classical density change, and randomness originates from the deterministic forward mapping of an initial classical density distribution. Entanglement corresponds to a sum of classical particle actions mapping to a tensor product of spinors, and in the Einstein-Podolsky-Rosen experiment, while Bell's inequalities are violated, from this perspective there is indeed a hidden variable in the form of a complex spinor. A wave function could be computed based on the known action solution of the Schwarzschild metric.

Joint work with Winfried Lohmiller.