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Quantum MechanicsDe Broglie's hypothesis gave both mathematical support and a convenient physical analogy to account for the quantized states of electrons within an atom, but his atomic model was still incomplete. Within a few years, though, physicists Werner Heisenberg and Erwin Schrodinger, working independently of each other, built upon de Broglie's concept of a matterwave duality to create more mathematically rigorous models of subatomic particles. This form of “uncertainty” relationship exists in areas other than quantum mechanics. As discussed in the “MixedFrequency AC Signals” chapter in volume II of this book series, there is a mutually exclusive relationship between the certainty of a waveform's timedomain data and its frequencydomain data. In simple terms, the more precisely we know its constituent frequency(ies), the less precisely we know its amplitude in time, and vice versa. To quote myself: In order to precisely determine the amplitude of a varying signal, we must sample it over a very narrow span of time. However, doing this limits our view of the wave's frequency. Conversely, to determine a wave's frequency with great precision, we must sample it over many cycles, which means we lose view of its amplitude at any given moment. Thus, we cannot simultaneously know the instantaneous amplitude and the overall frequency of any wave with unlimited precision. Stranger yet, this uncertainty is much more than observer imprecision; it resides in the very nature of the wave. It is not as though it would be possible, given the proper technology, to obtain precise measurements of both instantaneous amplitude and frequency at once. Quite literally, a wave cannot have both a precise, instantaneous amplitude, and a precise frequency at the same time. The minimum uncertainty of a particle's position and momentum expressed by Heisenberg and Schrodinger has nothing to do with limitation in measurement; rather it is an intrinsic property of the particle's matterwave dual nature. Electrons, therefore, do not really exist in their “orbits” as precisely defined bits of matter, or even as precisely defined waveshapes, but rather as “clouds”  the technical term is wavefunction  of probability distribution, as if each electron were “spread” or “smeared” over a range of positions and momenta. This radical view of electrons as imprecise clouds at first seems to contradict the original principle of quantized electron states: that electrons exist in discrete, defined “orbits” around atomic nuclei. It was, after all, this discovery that led to the formation of quantum theory to explain it. How odd it seems that a theory developed to explain the discrete behavior of electrons ends up declaring that electrons exist as “clouds” rather than as discrete pieces of matter. However, the quantized behavior of electrons does not depend on electrons having definite position and momentum values, but rather on other properties called quantum numbers. In essence, quantum mechanics dispenses with commonly held notions of absolute position and absolute momentum, and replaces them with absolute notions of a sort having no analogue in common experience. Even though electrons are known to exist in ethereal, “cloudlike” forms of distributed probability rather than as discrete chunks of matter, those “clouds” have other characteristics that are discrete. Any electron in an atom can be described in terms of four numerical measures (the previously mentioned quantum numbers), called the Principal, Angular Momentum, Magnetic, and Spin quantum numbers.


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