Titlebook: Mathematics of Particle-Wave Mechanical Systems; James M. Hill Book 2022 The Editor(s) (if applicable) and The Author(s), under exclusive

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Relation with Quantum Mechanics,gives . = −(.∕. + . ), and this is precisely the structure of the standard operator relations of quantum mechanics. That is, the established structure of the conventional operators of quantum mechanics is embodied in the present approach and arises from conservation of energy.

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Introduction, background issues which is followed by two brief sections on special relativity and quantum mechanics that emphasise the importance that any new theories might sensibly be cognisant of the considerable successes of existing theories. The section thereafter introduces the general idea of de Broglie

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Special Relativity,n of Newton’s second law. The word special alludes to invariance under transformations relating constant relative velocity frames of reference, which is in contrast to general relativity which relates to invariance under arbitrary space-time coordinate transformations. The first section deals with t

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Special Results for One Space Dimension,hapter we present a number of additional general results which apply for de Broglie particle-wave mechanical systems for a single Cartesian spatial dimension. We need to emphasise that these results might be termed special or privileged in the sense that they are only applicable to a single Cartesia

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Derivations and Formulae,vious chapter. We first derive the solution and then present various details relating to the integrals and formulae for the de Broglie wave energy. As we have previously mentioned, even though the de Broglie wave energy is given simply by ., the determination of the wave energy as a function of velo

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