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When some fundamental new theory is published, derived work will be done "instantly", example from quantum mechanics:

1926 Schrödinger equation

1927 The first application of quantum mechanics to the diatomic hydrogen molecule

1928 The concept of the Bloch state

1928 Relativistic quantum mechanics

1940s Quantum electrodynmics.

But wave guide theory is only published in 1897 On the Passage of Electric Waves through Tubes

The above QM theories are much more "harder" than the theory of wave guide, then why is it published after such a long timer after Maxwell's equations were published?

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    $\begingroup$ Because passage of electric waves through tubes did not sound nearly as exciting as the radical change in understanding the fundamental structure of matter, and so attracted fewer people? The strange behavior of the speed of light, which did have fundamental import, got a lot more attention during that period. $\endgroup$
    – Conifold
    Jan 19, 2021 at 6:55
  • $\begingroup$ @Conifold After QM this really seems not that exciting. But before QM and SR, isn't new thing as EM and its relation with light eciting enough? Then the behavior of EM, under free space and constrained space (including wave guide), and re-research of all light phenomenon based on EM, shoulde be unbelievable exictin that that time. $\endgroup$
    – jw_
    Jan 21, 2021 at 2:21
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    $\begingroup$ This question would be much more understandable if it included the dates when quantum mechanics and wave guide theory were published. I.e. it's not obvious what '"instantly"' and 'such a long time' mean. $\endgroup$
    – Ray Butterworth
    Nov 22, 2021 at 14:14

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This is not an answer but a viewpoint to examine: EM theory as we now know it was largely developed by Oliver Heaviside in the 1880s and 1890s from Maxwell's somewhat awkward formulation (it's tedious). Heaviside began as a telegraphy technician without much formal education, none in science or math. But he showed great physical intuition from experiments with long distance telegraphy. He also taught himself the math (extremely difficult in those days compared to the present); he eventually became a frequent and respected contributor to telegraphy and EE journals. Josiah Willard Gibbs transformed (contributed to?) Heaviside's mathematical approach via vector calculus. See the Wikipedia bio on Heaviside (I'm a physicist and found it eye opening: we were never taught anything about him). The other part to your question is that waveguides depend on EM wave generation, which was not so well understood in the 1880s and 1890s until after these mathematical transformations began and better test instruments were invented. Remember that Heinrich Hertz did not prove that EM waves actually did exist until about 1887 based on his interpretation of Maxwell's work. Also note that non-trivial math was not so widely used in professional science and engineering circles as they are today. Penetration of mathematical ideas (on which waveguides depend) was much slower in the late 19th century compared to just fifty years later. For example, electrical engineers were not universally taught calculus until about World War II (I've seen some of the textbooks). Yes, some practical understanding was achieved by analog reasoning and experimentation but a full appreciation and exploitation eventually required the math. HTH.

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