In this paper, I will review some inadequacies of Schrödinger equation. Then I will discuss George Shpenkov’s interpretation of classical wave equation and two other authors’ wave equations. According to Shpenkov, the classical wave equation is able to derive a periodic table of elements -which is close to Mendeleyev’s periodic table-, and also other phenomena related to the structure of molecules. It is argued here that one may arrive at new energy methods using this classical wave equation as starting point. It is suggested that Shpenkov’s interpretation of classical wave equation can complement Schrödinger equation.
In a recent paper, it has been argued that QM can arise from classical cellular automata. This is a fresh approach started by some authors including Prof. Gerard ‘t Hooft. Nonetheless, in a previous paper, we have reviewed some inadequacies of Schrodinger equation, hence the entire wave mechanics. According to Shpenkov, the classical wave equation is able to derive a periodic table of elements -which is close to Mendeleyev’s periodic table-, and also other phenomena related to the structure of molecules. It is suggested that Shpenkov’s interpretation of classical wave equation can complement Schrodinger equation. Therefore in this paper we will discuss how we can arrive to a cellular automaton molecular model starting from classical wave equation, as an alternative to cellular automata based QM.
In light of the fact that our world requires new energy supply in order to replace fossil based energy, then it seems that new theory is badly needed – because it is often true that new energy requires new theory. And new theory can only come from new insights. In this paper, I will review the inadequacy of spherical solution of Schrodinger equation to say anything about the structure of molecules. It is a common fact, that the spherical solution of Schrodinger equation is hardly discussed properly in many quantum mechanics textbooks, with excuse that it is too complicated. Then I will discuss George Shpenkov’s wave equation which is able to derive the periodic table of elements, and other phenomena related to the structure of molecules, which is an elusive dream from the viewpoint of quantum mechanics. It is argued here that one can expect to arrive at new energy methods using this wave equation as starting point, for instance by virtue of resonance vibration theory. Nonetheless, it is not our view here that the Shpenkov’s wave equation can substitute wave mechanics completely, instead we prefer to say that it can be a complementary approach of wave mechanics. By referring to Schrodinger’s dream in his 1926 paper to find connection between his wave mechanics and vibration frequency, I think that Shpenkov’s wave equation can fulfill that dream.
As its name suggests, Schrodinger’s equation is the brain child of Schrodinger and was first disclosed in 1926 in a paper entitled An Undulatory Theory of the Mechanics of Atoms and Molecules . Schrodinger begins by considering the dynamics of a particle moving through a force field. The Schrodinger’s equation is arrived at in an alternative heuristic path modeled after Haken. The Schrodinger’s equation is a wave equation that incorporates classical particle concepts, and classical wave function concepts, in its derivation. In other words, a heuristic approach to Schrodinger’s equation utilizes Max Planck’s quantum energy, classical kinetic energy of a free particle, and the classical “wave functions of ordinary wave optics.” Schrodinger’s equation is capable of explaining all atomic phenomena except those involving magnetism and relativity.
Abstract In this paper I explain how I usually introduce the Schrödinger equation during the quantum mechanics course. My preferred method is the chronological one. Since the Schrödinger equation belongs to a special case of wave equations I start the course with introducing the wave equation. The Schrödinger equation is derived with the help of the two quantum concepts introduced by Max Planck, Einstein, and de Broglie, i.e. the energy of a photon E = ћ ω and the wavelength of the de Broglie wave λ = h / p . Finally, the difference between the classical wave equation and the quantum Schrödinger one is explained in order to help the students to grasp the meaning of quantum wavefunction Ψ ( r , t ) . A comparison of the present method to the approaches given by the authors of quantum mechanics textbooks as well as that of the original Nuffield A level is presented. It is found that the present approach is different from those given by these authors, except by Weinberg or Dicke and Wittke. However, the approach is in line with the original Nuffield A level one.
This study delves into the realm of Schrödinger equations and wave mechanics, aiming to see if they could provide a foundation comparable in generality to that formulated in the preceding chapter, and to bridge the gap between classical and quantum physics. It begins by deriving a family of Schrödinger-like equations. The study introduces an intuitive approach for deriving an entire spectrum of Schrödinger-like equations, encompassing classical and novel variants, through the utilization of the complex wave function and its conjugate, along with the assumptionsA01, A08. Examining the concepts of the complex wave function
ψ and the multi-vector wave function
Ψ reveals their equal generality, suggesting the applicability of Schrödinger-like equations in the context of multi-vectors, including both
ψ and the phase
Φ . To explore the correspondence principle between quantum and classical mechanics, a well-studied example is dissected in Section 2.4, necessitating the development of a suitable wave function (2.50). The use of the real function [1, (1.50)] to form the complex test function (2.50) is a logical step, and its substitution into the Schrödinger equations aims to yield an identity. The substitution of (2.50) reveals a discrepancy between the left and right sides of the Schrödinger equations (2.25, 2.26), highlighting their inadequacy in describing the classical mechanics example accurately. This observation underscores the limitations of classical Schrödinger equations and their departure from the correspondence principle. Consequently, a more comprehensive set of Schrödinger-like equations (2.58-2.68) is derived, rendering the previously considered equations (2.25, 2.26) irrelevant. Substituting the test function (2.50) into equations (2.58-2.68) demonstrates their soundness and suitability for the example, establishing the correspondence principle between classical and quantum mechanics. Our analysis indicates that the classical set [1, (1.4-1.6)] exhibits a higher degree of generality than the quantum one (2.58-2.68), thereby deferring the definitive validation of this assertion to forthcoming research endeavours. These findings underscore the potential significance of our framework in bridging the gap between quantum and classical mechanics, promising further exploration and validation in future studies.