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Primary Assumptions and Guidance Laws in Wave Mechanics

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Document pages: 14 pages

Abstract: In an article written by Louis deBroglie in 1959 (30 years after the Nobel prize rewarding his foundation ofWave Mechanics), the most challenging problem raised by the Bohr, Heisenbergand Born Standard Quantum Mechanics (SQM) was pointed out in the renunciationto describe “a permanent localization in space, and therefore a well-defined trajectory”for any moving particle. This challenge is taken up in the present paper,showing that de Broglie’s Primary Assumption p=hk, predicting the wave-particle duality, does alsoallow to obtain from the energy-dependent form of the Schrödinger and or Klein-Gordon equations the Guidance Laws pilotingparticles along well-defined trajectories. The energy-independent equations, on the other hand, may only give rise—both in SQM and in the Bohmian approach—to probabilistic descriptions, overshadowing the role of de Broglie’s matter waves in physical space.

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