### Abstract

We consider the limiting case ??0 of the Cauchy problem (Equation Presented) u_{?}(x,0) = exp[-S_{0}(x)/?] T_{0}(x); S_{0}, T_{0} independent of ?, for both real and pure imaginary ?. We prove two new theorems relating the limiting solution of the above Cauchy problem to the corresponding equations of classical mechanics (Equation Presented) These relationships include the physical result quantum mechanics ? classical mechanics as ??0. Copyright © 1977 American Institute of Physics.

Original language | English |
---|---|

Pages (from-to) | 2308-2315 |

Number of pages | 8 |

Journal | Journal of Mathematical Physics |

Volume | 18 |

Issue number | 12 |

Publication status | Published - 1976 |

## Fingerprint Dive into the research topics of 'Classical mechanics, the diffusion (heat) equation, and the Schrödinger equation'. Together they form a unique fingerprint.

## Cite this

Truman, A. (1976). Classical mechanics, the diffusion (heat) equation, and the Schrödinger equation.

*Journal of Mathematical Physics*,*18*(12), 2308-2315.