Special Results for One Space Dimension

James Hill
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James Hill: University of South Australia

Chapter Chapter 4 in Mathematics of Particle-Wave Mechanical Systems, 2022, pp 91-147 from Springer

Abstract: Abstract The purpose of this chapter is to illustrate the formal extension of Newton’s second law given by ( 3.4 ) in their simplest conceivable context. In this chapter 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 Cartesian spatial dimension and in the absence of any curvature effects. In some instances their generalisation may be straightforward while, in others, perhaps an entirely non-trivial matter. Nevertheless, even with this in mind, special exact results and consequences are always important and helpful in providing insight.

Date: 2022
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DOI: 10.1007/978-3-031-19793-2_4

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