The Schrödinger Realization of Quantum Mechanics

Daniel R. Bes

Yuchuan Wei

Laskin introduced the fractional quantum mechanics and several common problems were solved in a piecewise fashion. However, Jeng et al pointed out that it was meaningless to solve a nonlocal equation in a piecewise fashion and that all the solutions in publication were wrong except the solution for the delta function potential, which was obtained in the momentum space. Jeng's critique results in a crisis of fractional quantum mechanics, that is, in mathematics it is quite difficult to find solutions to the fractional Schrodinger equation and in physics there is no realization for the fractional quantum mechanics. In order to eliminate this crisis, this paper reports some analytic solutions to the fractional Schrodinger equation without using piecewise method, and introduces the relativistic Schrodinger equation as a realization of the fractional quantum mechanics. These two sister equations should be studied at the same time.

Nima Moshayedi

H. P. Laba, K. O. Chaban, V. M. Tkachuk

Equations describing TE and TM modes in planar waveguide with a position-dependent permittivity and permeability can be reduced to the Schrödinger equation. The condition allowing realization of the supersymmetric quantum mechanics in waveguide is found. TM modes in optical waveguides are described by the Schrödinger equation with a position-dependent mass.

Francis T. S. Yu

Schrödinger’s quantum mechanics is a legacy of Hamiltonian’s classical mechanics. But Hamiltonian mechanics was developed from an empty space paradigm, for which Schrödinger’s equation is a timeless (t = 0) or time-independent deterministic equation, which includes his fundamental principle of superposition. When one is dealing Schrödinger equation, it is unavoidable not to mention about Schrödinger ‘s cat. Which is one of the most elusive cats in modern science since disclosed the half-life cat hypothesis in 1935. The cat is alive or not had been debated by score of world renounced scientists it is still debating. Yet I will show Schrödinger ‘s hypothesis is not a physically realizable hypothesis, for which it has nothing for us to debate about. But quantum communication and computing rely on qubit information algorithm, I will show that qubit information logic is as elusive as Schrödinger’s cat. It exists only within an empty space, but not exists within our temporal (t > 0) universe. Since there is always a price to pay within our universe, I will show that every physical subspace needs a section of time ∆t and an amount of energy ∆E to create and it is not free. Although, double slit hypothesis had been fictitiously confirmed that superposition principle exists, but I will show that double-slit postulation is another non-physically realizable hypothesis that had let us to believing superposition principle is actually existed within our time–space. Yet one of the worst coverup must be particles behaved differently within a micro space to justify the spooky superposition principle, which is one of greatest quantum conspiracy in modern science. Nevertheless, the art of quantum mechanics is all about a physically realizable equation, we see that everything existed within our universe, no matter how small it is, it has to be temporal (t > 0) which includes all the laws, principles, and equations. Otherwise, it is virtual as mathematics is since Schrodinger equation is mathematics, but mathematics is not equaled to science. Finally, when science turns to virtual reality for solution it is not a reliable answer. But when science turns to physical reality for an answer it is a reliable solution.