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| Format: | Recurso digital |
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Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.18528977 |
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Table of Contents:
- <p>We show that the de Broglie (Prince) equation λ p = h naturally produces two conjugate momenta—a group momentum p_group = mv_n and a phase momentum p_phase = mc^2/v—whose product equals the square of the photon momentum:<br>p_phase ×p_group = p^2(ϕ).This reformulation eliminates the superluminal phase velocity problem that has plagued wave mechanics since 1924. We first derive the constancy of Planck’s constant from the classical work equation and the Leibniz product rule, requiring no quantum postulates. The photon boundary at v = c fixes H = h and eliminates the integration constant, rendering the assumption v = 0 unnecessary. Velocity quantization v_n = c (n−1)/(n+1) emerges from first principles, producing discrete momentum levels where pn = mvn recovers classical mechanics at each level. The imaginary unit 'i' emerges algebraically when the Prince equation forbids rest. By expressing the wave’s phase structure as a momentum rather than a velocity, the physical ontological reality of matter waves becomes manifest without any quantity exceeding c.</p>