Wave-particle duality revitalized: Rectifications, verifications, and applications

The proposed paper calls attention towards the unobserved mathematical and conceptual inadequacies in de Broglie's theory of matter waves. Matter waves' frequency and phase velocity expressions are primarily shown to be inconsistent and have emerged on account of inappropriate concepts presumed by de Broglie. Rectifications in these concepts are presented and the modified frequency and phase velocity expressions are introduced. The proposed modified expressions (for matter waves) have been shown to overcome all the inadequacies and negations confronted by de Broglie's expressions. On the basis of the proposed concepts, a wave-particle duality picture is presented, which elucidates the ambiguous questions coupled with the wave-particle duality existing in the literature. Consequently, particle type nature is shown to be a characteristic of waves only, independent from the presence of matter. The correction introduced in the frequency expression for matter waves leads to the variation in the wave function expression for a freely moving particle and its energy operators, with appropriate justifications provided in the paper. Application of the modified wave function is provided by deriving the fundamentally correct Schrödinger's equation, Klein‐Gordon's equation and Dirac's equation. The satisfactory derivations of these equations provide a confirmation step for the proposed concepts. Finally, concrete mathematical proof for the proposed modified frequency and phase velocity expressions are also provided.