The author has worked with high-resolution transmission electron microscope for many years, which provides the most direct evidence of wave-particle duality. This relates to Crookes and J. J. Thomson's cathode rays tubes to determine that electron beams are of particle nature. This also relates to Röntgen's discovery that when an electron beam in the cathode rays tube strikes the glass wall, it produces X-rays with extremely high penetrating power. This behavior is consistent with Maxwell-Lorentz’s electrodynamics that electromagnetic waves must be produced whenever electricity carriers alter their velocity. The wave-particle duality proposed by de Broglie refers to accelerated electron beam, rather than single electron. De Broglie emphasized that the crystallographic diffraction pattern produced by his electron beam was completely consistent with the crystallographic diffraction pattern of von Laue transmission X-rays. Therefore, he proposed that electrons possess wave-particle duality. This is actually the selected area electron diffraction pattern in transmission microscope. It is X-rays, not the waves of the electrons themselves to produce diffraction pattern. Once we understand how X-rays are produced, we'll immediately grasp this point. He extended the wave-particle duality to all matter and light. This crucial physical property has no connection to the experimental results of numerous scientists previously. Schrödinger directly introduced de Broglie's electron beam behavior into electron wave in atoms. It was just at this stage that illogical reasoning occurred, making the quantum theory increasingly difficult to understand.
Firstly, de Broglie's electron transmission crystal diffraction pattern is formed by X-rays, because his single-crystal sample at that time was definitely much larger than 100 nanometers, which electrons cannot penetrate. What penetrates are the X-rays. Lenard et al. had already determined that X-rays do not contain negatively charged electrons. Secondly, wave-particle duality sometimes mix together and sometimes separate (Lenard). These are two concepts: electron beam (short penetrating depth) and X-rays (long penetrating depth), not that electrons themselves possess two properties. The formula λ= h/p proposed by de Broglie is a simple way to estimate the wavelength of the X-rays created by electron beam at certain velocity. Under the experimental conditions at the time, most accelerating voltages were 30 kV, and electron speeds were 1/3 the speed of light. Schrödinger's atomic model fully embraces wave-particle duality, treating the electron as a three-dimensional standing wave around the nucleus. Therefore, this wavelength must be smaller than the size of an atom (1 Å). The velocity of an electron in an atom would then be 10⁸ m/s, circling the Earth four or five times per minute. Is it possible that, under such high speeds, electrons would appear around the atomic nucleus according to probability?
Can we pass on such Schrödinger’s theory to future generations? This is a questioning of the soul of every scientist.