### Abstract

We obtain some new results on the role played by the classical action in nonrelativistic quantum mechanics. The results are of the same genre as those derived previously by Nelson from the Trotter product formula. Here we work with the exact expression for the classical action not the approximate one as used by Nelson. Our results give a precise relationship between classical mechanics and quantum mechanics for a fairly wide class of potentials. The results are derived by using the properties of a new definition of the Feynman path integral J introduced in an earlier paper. Copyright © 1977 American Institute of Physics.

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

Pages (from-to) | 1499-1509 |

Number of pages | 11 |

Journal | Journal of Mathematical Physics |

Volume | 18 |

Issue number | 7 |

Publication status | Published - 1976 |

### Fingerprint

### Cite this

*Journal of Mathematical Physics*,

*18*(7), 1499-1509.

}

*Journal of Mathematical Physics*, vol. 18, no. 7, pp. 1499-1509.

**The classical action in nonrelativistic quantum mechanics.** / Truman, Aubrey.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The classical action in nonrelativistic quantum mechanics

AU - Truman, Aubrey

PY - 1976

Y1 - 1976

N2 - We obtain some new results on the role played by the classical action in nonrelativistic quantum mechanics. The results are of the same genre as those derived previously by Nelson from the Trotter product formula. Here we work with the exact expression for the classical action not the approximate one as used by Nelson. Our results give a precise relationship between classical mechanics and quantum mechanics for a fairly wide class of potentials. The results are derived by using the properties of a new definition of the Feynman path integral J introduced in an earlier paper. Copyright © 1977 American Institute of Physics.

AB - We obtain some new results on the role played by the classical action in nonrelativistic quantum mechanics. The results are of the same genre as those derived previously by Nelson from the Trotter product formula. Here we work with the exact expression for the classical action not the approximate one as used by Nelson. Our results give a precise relationship between classical mechanics and quantum mechanics for a fairly wide class of potentials. The results are derived by using the properties of a new definition of the Feynman path integral J introduced in an earlier paper. Copyright © 1977 American Institute of Physics.

M3 - Article

VL - 18

SP - 1499

EP - 1509

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 7

ER -