resonance, harmonic oscillator, quantum, pontryagin dualism
Ideal Resonance does not fade and thus it is as it were out of time So the corresponding Planck QUANTUM which determines the STATIONARY Allowed States of Energy is simply a reflection of the Ideal Resonance which Quantum Mechanics used on the example of the Mechanical Harmonic Oscillator And the fundamental difference of QUANTUMS is only that for frequencies not equal to zero and their minimum energy of the Resonance-Quantum has a finite non-zero initial value which also determines the minimum distance between the allowed energy levels At the same time the internal structure of the QUANTUM can be not only electromagnetic like Planck s and not only acoustic like Einstein s but also be determined by the so-called de Broglie matter waves But in order to remove any mysticism from QUANTUMS one must UNDERSTAND that the DUALISM introduced by them is determined by Pontryagin s functional connection of the ELEMENTARY PARTICLE and the Packet of Waves that form it
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