Abstract
The derivation of the time-independent Schrödinger equation is based on a new approach to basic physics. The concept of fundamental particles with associated wave properties as the basic elements of physics is abandoned. Instead, it is hypothesized that the universe is a pure wave system and the constructive interference peaks of the wave system are the elementary particles. Based on this hypothesis, an elementary particle moving in the rest system may be represented in the moving system by a stationary constructive interference peak. Then, the Schrödinger equation is obtained by a Lorentz transformation of the stationary constructive interference peak from the moving system to the rest system.
Two new results are obtained. First. two identical and independent Schrodinger equations are derived instead of one as expected. Applying both independent Schrodinger equations to an atom.. an additional independent set of states is obtained. Therefore. the number of states now agrees with the experimentally determined number of states in atoms without consideration of the two spin states of the electron. Second, the electron in the ground state of the hydrogen atom is found to oscillate radially over a very small distance around the average position of the electron.
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Andrews, T.B. (1997). Derivation of the Schrödinger Equation. In: Jeffers, S., Roy, S., Vigier, JP., Hunter, G. (eds) The Present Status of the Quantum Theory of Light. Fundamental Theories of Physics, vol 80. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5682-0_19
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DOI: https://doi.org/10.1007/978-94-011-5682-0_19
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