Astrit Denaj, Valbona Tahiri, Jorgo Mandili



The Quantum of Action and the Principle of Least Action

pdf PDF


In 1900, to avoid the contradictions between classical theory and experiment, in the study of the distribution of blackbody radiation energy law, Planck, with a genius intuition, stated that the classical law of interaction should be abandoned. Given the fact that this law is based on the notions of continuous energy exchange, Planck proposed that this energy exchange occurs in discrete and indivisible portions, which he called "energy quanta". He showed that the quantum of energy is proportional to the frequency ν of the radiation, which is well-known today as the Planck constant. It has the dimensions of action (energy x time) or (momentum x length). Planck realized that the quantum hypothesis was essentially not an energy hypothesis, but an action hypothesis. The quantum of energy for radiation makes sense only for periodic phenomena that have a definite frequency. But there is no doubt that Planck realized that the element of action, should have a more fundamental meaning both for non-periodic and non-stationary phenomena. He "felt" that the physical meaning of the action element could be harmonized only with the help of the principle of least action which governs all fundamental phenomena in nature. Talking about this harmony between the quantum hypothesis and the principle of least action, Planck showed that this principle should be given a more general form, which makes it applicable even to discrete phenomena. Planck's hypothesis about quanta introduces into the principle of least action a fundamental condition: complete action can always be an integer multiple of Planck's constant. Atomic systems of various natures can now be described in terms of action, and hence the quantum conditions of motion in the atomic world (Bohr-Sommerfeld conditions) can be derived, and further, according to Feynman's imagination, the principle of action on small can be interpreted in a more realistic conception as the principle of maximum probability, which means that the single trajectory, is the most probable. The principle of least action is statistical. The analysis and general methodological-scientific of the above problem are the object of this article.


Classical theory, Planck’s hypothesis, quanta, principle of least action, integral of action


Cite this paper

Astrit Denaj, Valbona Tahiri, Jorgo Mandili. (2023) The Quantum of Action and the Principle of Least Action. International Journal of Applied Physics, 8, 32-40


Copyright © 2023 Author(s) retain the copyright of this article.
This article is published under the terms of the Creative Commons Attribution License 4.0