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My opinion about Schrodinger equation

已有 4906 次阅读 2010-3-25 09:24 |个人分类:观点和方法|系统分类:观点评述| change

这是我在SFN上的新贴,提出了我个人对量子和薜定谔方程的理解,请多指教。

Spectroscope is produced by the change of atomic and molecular structure, and can be explained by the consequence from Schrödinger equation. That means the mathematical expression Schrödinger equation describes the relationship between the electromagnetic radiation and physical quantities while the structure change. Therefore, Schrödinger equation is a condition equation of the change of atomic and molecular structure.

In my manuscript, it was proved that there is a natural steady circular orbit (ground state) of the electron for isolated hydrogen atom according to electromagnetism. When the resonance of the ground orbit takes place, hydrogen atom is at an excited state with higher energy. This effect is so-called modal response of hydrogen atomic structure by means of structure mechanics, and the modal frequencies of the electronic orbit are determined by the ground state and the mechanical properties of central-field caused by the proton.

By classical theory, the two-body system of hydrogen atom could be described by the model of the electron with reduced mass rotates around proton. The ground circular motion of the electron could be described by motion equation or orbit equation, and standing wave equation could be also selected to treat the circle orbit because the circle orbit may be understood as a special standing wave with wavelength 2πr and invariable amplitude r (r is the radius of the circle orbit). It is easy to get the equation of the ground electron in form of standing wave, and the modal frequencies of ground orbit of the electron could be deduced from solution of that standing wave equation. In this case, the standing wave equation of the electron is mathematically introduced to treat the resonance of the ground orbit, but doesn’t mean the electron moves as a standing wave.

For ground state of hydrogen atom, if we select the ground orbit of the electron as reference to describe the other modal orbits, the radius of ground orbit of hydrogen atom (bohr radius a0) becomes a physical constant and unit for description of other modal orbits, and Schrödinger equation of hydrogen atom would be deduced from the ground electronic equation in form standing wave. Meanwhile the mathematical relations were also obtained, E=hν, Planck constant h is related to bohr radius of hydrogen atom, charge and reduced mass of electron.

Therefore, the resonance equation of ground hydrogen atom in form standing wave is equivalent to Schrödinger equation, and the physical quantities from Schrödinger equation should be expressed by that of ground state of hydrogen atom. The solution of Schrödinger equation is relative result comparing to that of ground state of hydrogen atom.

For complex atoms, the motions of the electrons are similar to hydrogen atom, and could be treated with central-field model. So, the solution of hydrogen atom provides the foundation for description of the complex atoms.

By my opinion, quantization phenomenon in atomic and molecular world is related to the resonance effect of their orbit structure. To select the ground state of hydrogen atom as reference, this phenomenon could be describe with Schrödinger equation, and Planck hypothesis is a certain mathematical relation with it.



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