In this paper, we show that the generalization of the parabolic Schrodinger equation to hyperbolic partial differential equations leads to possibility of the study of consciousness on the quantum level. In our hypothesis, consciousness is operated by wave equation which do not dependent on the mass of particle.
Scientists used to believe until recently that the consciousness/mind/thought is a purely metaphysical concept and hence has nothing to do with science. However recent scientific research both theoretically and also experimentally strongly imply that consciousness/mind/thought is in fact a physical concept and could be investigated by scientific means. This very exciting and revolutionary approach recently attracted much interest to the subject. However, the nature of the subject needs interdisciplinary collaboration of especially neuroscientists and physicists/quantum physicists and also possibly psychiatrists, philosophers and more. This paper is therefore organized and prepared in order to serve to bridge the gap between especially neuroscientists and quantum physicists. The present work in particular deals with the Schrodinger wave equation and wave function that lie right on the spine of the entire quantum physics and must be understood clearly before any further steps. More specifically, the paper focuses on philosophical approaches to consciousness, Schrodinger wave equation, wave function and its physical meaning, generalization of the wave function and finally general remarks on the relation between consciousness/mind and quantum physics. Scientific and philosophical background is momentarily fulfilled in advance to enhance the emotional willingness of the readers.
The problem of d-dimensional Schrödinger equations with a position-dependent mass is analyzed in the framework of first-order intertwining operators. With the pair (H,H1) of intertwined Hamiltonians one can associate another pair of secondorder partial differential operators (R,R1), related to the same intertwining operator and such that H (resp. H1) commutes with R (resp. R1). This property is interpreted in superalgebraic terms in the context of supersymmetric quantum mechanics (SUSYQM). In the two-dimensional case, a solution to the resulting system of partial differential equations is obtained and used to build a physically-relevant model depicting a particle moving in a semi-infinite layer. Such a model is solved by employing either the commutativity of H with some second-order partial differential operator L and the resulting separability of the Schrödinger equation or that of H and R together with SUSYQM and shape-invariance techniques. The relation between both approaches is also studied.
In this present work, we study the approximate solution of the Schrodinger equation with hyperbolic function position-dependent mass for a symmetrical Modified Poschl-Teller potential. We consider the system influenced by the external hyperbolic magnetic and Aharonov-Bohm (AB) forces. By using the Laplace transform method, the second-order differential equation of the Schrodinger equation is reduced to a first-order differential equation and so the eigenfunction and energy eigenvalues are obtained. The behavior of the bound state energy levels was demonstrated and analyzed using the computational method for various values of the potential parameter, mass parameter, external magnetic force, and AB force. Moreover, the thermomagnetic properties of the system were analyzed for H2, LiH, and HCl diatomic particles, involving the vibrational mean energy, vibrational free energy, vibrational entropy, specific heat capacity, magnetization, magnetic susceptibility, and persistent current.
We present a simplified analog quantum simulation protocol for preparing quantum states that embed solutions of parabolic partial differential equations, including the heat, Black-Scholes and Fokker-Planck equations. The key idea is to approximate the heat equations by a system of hyperbolic heat equations that involve only first-order differential operators. This scheme requires relatively simple interaction terms in the Hamiltonian, which are the electric and magnetic dipole moment-like interaction terms that would be present in a Jaynes-Cummings-like model. For a d-dimensional problem, we show that it is much more appropriate to use a single d-level quantum system - a qudit - instead of its qubit counterpart, and d+1 qumodes. The total resource cost is efficient in d and precision error, and has potential for realisability for instance in cavity and circuit QED systems.