The “quantum” world, within the framework of which “outstanding” scientific discoveries are being made now, is built on initially laid nonsense. Quantum theory was initially built on incorrect adjustment by Schrödinger of two-dimensional “solutions” of the One-dimensional harmonic oscillator equation. These are the consequences of this fitting and “excited minds.” This is the reason why quantum mechanics is not necessary to UNDERSTAND, but it is necessary to ACCEPT. But they accepted and canonized, as is shown in this work, non-physical, rough, approximate solutions. And it is on the basis of these solutions that electron orbitals, widely used in fundamental and applied science, are constructed. So the “Terrible Secret” of the theorists is that in fact without having a basic model they are exclusively engaged in fitting Schrödinger’ssolutions.
The “quantum” world, within the framework of which “outstanding” scientific discoveries are being made now, is built on initially laid nonsense. Quantum theory was initially built on incorrect adjustment by Schrödinger of two-dimensional “solutions” of the One-dimensional harmonic oscillator equation. These are the consequences of this fitting and “excited minds.” This is the reason why quantum mechanics is not necessary to UNDERSTAND, but it is necessary to ACCEPT. But they accepted and canonized, as is shown in this work, non-physical, rough, approximate solutions. And it is on the basis of these solutions that electron orbitals, widely used in fundamental and applied science, are constructed. So the “Terrible Secret” of the theorists is that in fact without having a basic model they are exclusively engaged in fitting Schrödinger’ssolutions.
The Schrödinger equation describes the basic physical models in a very contradictory way. And its canonization, which gives a catastrophic divergence of the energy of electronic levels with an increase in the mass of an atom, in principle, stalled the development of science. Nevertheless, it allowed, albeit roughly, to systematize and describe many phenomena of the microworld, primarily the hydrogen atom. And approximate descriptions of many “quantum” effects were obtained, but with the use of numerous adjustable parameters. So the bottom line from the century of development of quantum theory (QT) is, in fact, the development of some quantum mechanical methods.
Toward the end of the nineteenth century, it became clear that some experiments cannot be explained on the basis of known physics, now referred to as classical physics. In 1900, Max Planck was able to correctly describe the distribution of blackbody radiation energy as a function of wavelength λ or frequency ν = c/λ. He had to accept the existence of energy packets (quanta) with energy E = hν. A few years later, Albert Einstein found that this unexpected relation between energy and frequency is also necessary in order to understand photoemission from metallic surfaces. A decade later, Niels Bohr arrived at the correct equation for the electronic spectrum of the hydrogen atom by applying “quantum conditions” on the motion of the electron around the nucleus and the Planck’s relation E = hν on the energy difference between the energy levels (1916). A decade later, Heisenberg, Born, and Jordan introduced “quantum mechanics” and de Broglie and Schrödinger (1925-1926) introduced “wave mechanics.”
A hundred years ago, physics underwent one of its most dramatic transformations - a paradigm shift that fundamentally changed our understanding of nature. Over the course of several revolutionary months in 1925 and early 1926, quantum mechanics emerged as a new, foundational theory of the microscopic world. With the publication of key papers by Werner Heisenberg and Erwin Schrödinger, the theoretical framework was established that radically redefined our perception of physical reality. These works demonstrated that atoms and subatomic particles do not obey the laws of classical mechanics, but instead follow entirely new, quantum laws. Born in those intense months, quantum mechanics became one of the cornerstones of modern physics and a lasting source of inspiration in both theoretical and applied sciences. This paradigmatic shift opened new avenues of research and laid the groundwork for scientific discoveries that continue to shape our understanding of nature today. This paper is dedicated to those pivotal historical moments - the months in which science made one of its deepest leaps and most consequential strides in comprehending the world.
Inadequate descriptions of atoms and molecules by the methods of classical physics led researchers to propose new ways to describe physical reality, giving birth to a totally new science, quantum mechanics. The methods of quantum mechanics are based on the introduction of a wave function, whose physical meaning is related to the probability of finding a certain particle, at a certain time in a volume element, positioned between x and x + dx in the x = direction, between y and y + dy in the y = direction, and between z and z + dz in the z = direction at certain time t. This wave function Ψ satisfies the Schrödinger equation, (−2mℏ2∇2+v)Ψ=EΨ,ℏ=2πh, or for short, HΨ = EΨ, where H, the Hamiltonian operator, is defined by the expression H=−2mℏ2∇2+V; h is Planck’s constant; ∇2 is the sum of the partial second derivatives with respect to x, y, and z; m is the mass of the particle; and V is the potential energy of the system. The Hamiltonian H represents the quantum equivalent of the sum of the kinetic energy and potential energy, with V being the potential energy operator and 2m−ℏ2∇2 the kinetic energy operator. Finally, E is the total energy of the system and is a number, not an operator.
The initial purpose is to add two physical origins for the outstandingly clear mathematical description that Dirac has left in his Principles of Quantum Mechanics. The first is the “internal motion” in the wave function of the electron that is now expressed through dispersion dynamics; the second is the physical origin for mathematical quantization. Bohr’s model for the hydrogen atom was “the greatest single step in the development of the theory of atomic structure.” It leads to the Schrodinger equation which is non-relativistic, but which conveniently equates together momentum and electrostatic potential in a representation containing mixed powers. Firstly, we show how the equation is expansible to approximate relativistic form by applying solutions for the dilation of time in special relativity, and for the contraction of space. The adaptation is to invariant “harmonic events” that are digitally quantized. Secondly, the internal motion of the electron is described by a stable wave packet that implies wave-particle duality. The duality includes uncertainty that is precisely described with some variance from Heisenberg’s axiomatic limit. Harmonic orbital wave functions are self-constructive. This is the physical origin of quantization.