Schrodinger Quantum Research Articles

A Tiny, Counterintuitive Change to the Mathematics of the Schrodinger Wave Packet and Quantum ElectroDynamics Could Vastly Simplify How We View Nature


 
 
 This article proposes that an unexpected approach to the mathematics of a Schro ̋dinger wave packet and Quantum Electro-Dynamics (QED), could vastly simplify how we perceive the world around us. It could get rid of most if not all quantum weirdness. Schro ̋dinger’s cat would be gone. Even things that we thought were unquestionably true about the quantum world would change. For example, the double slit experiment would no longer support wave particle duality. Experiments that appeared to say that entangled particles can communicate instantaneously over great distances, would no longer say that. Although the tiny mathematical change is counterintuitive, Occam’s razor dictates that we consider it because it simplifies how we view Nature in such a pervasive way. The change in question is to view a Schro ̋dinger wave packet as part of a larger Elementary Wave traveling in the opposite direction. It is known in quantum mechanics that the same wave can travel in two countervailing directions simultaneously. Equivalent changes would be made to QED and Quantum Field Theory. It is known in QM that there are zero energy waves: for example, the Schro ̋dinger wave carries amplitudes but not energy.
 
 

Perturbative approach to the entanglement entropy and the area law in Fock and polymer quantization

The area dependence of entanglement entropy of a free scalar field is often understood in terms of coupled harmonic oscillators. In Schrodinger quantization, the Gaussian nature of ground state wave-function for these oscillators is sufficient to provide the exact form of the reduced density matrix and its eigenvalues, thus giving the entanglement entropy. However, in polymer quantization, the ground state is not Gaussian and the formalism which can provide the exact analytical form of the reduced density matrix is not yet known. In order to address this issue, here we treat the interaction between two coupled harmonic oscillators in the perturbative approach and evaluate the entanglement entropy in Schrodinger and polymer quantization. In contrary to Schrodinger quantization, we show that in high frequency regime the entanglement entropy decreases for polymer quantization keeping the ratio of coupling strength to the square of individual oscillator frequency fixed. Furthermore, for a free scalar field, we validate the area dependence of entanglement entropy in Fock quantization and demonstrate that polymer quantization produces a similar area law.

Inverse Square Law in Spectrally Bounded Quantum Dynamics

The object of the paper is to formulate Quantum (Schrodinger) dynamics of spectrally bounded wavefunction. The Nyquist theorem is used to replace the wavefunction with a discrete series of numbers. Consequently, in this case, Schrodinger dynamics can be formalized as a universal set of ordinary differential Equations, with universal coupling between them, which are related to Euler’s formula. It is shown that the coefficient (m, n) is inversely proportional to the distance between the points n and m. As far as we know, this is the first time that this inverse square law was formulated.

Hamiltonian Approach to Secondary Quantization

Structures and objects used in Hamiltonian secondary quantization are discussed. By the secondary quantization of a Hamiltonian system ℋ, we mean the Schrodinger quantization of another Hamiltonian system ℋ1 for which the Hamiltonian equation is the Schrodinger one obtained by the quantization of the original Hamiltonian system ℋ. The phase space of ℋ1 is the realification ℍR of the complex Hilbert space ℍ of the quantum analogue of ℋ equipped with the natural symplectic structure. The role of a configuration space is played by the maximal real subspace of ℍ.

Semiclassical spectral series of a quantum Schrödinger operator corresponding to a singular circle composed of equilibria

On a two-dimensional surface, a Schrodinger operator is considered with a potential whose critical points form a closed curve. We pose the problem of describing the semiclassical spectral series corresponding to this curve. The standard construction for describing the spectral series corresponding to isolated nondegenerate equilibria or to periodic trajectories of Hamiltonian systems is not applicable in this situation. In the paper, a description of semiclassical solutions of the spectral problem for the quantum Schrodinger operator that correspond to nonisolated equilibria are presented and, to calculate the splitting of the eigenvalues, it turns out to be necessary to find the spectral series with a higher order of accuracy than it is usually required.

Science and the myth of information

In this article, we show the mythical relationship between science and information. Since every substance has a price-tag or price-tags of information which includes all the building blocks in our universe, one can not simply ignore information when dealing with science. We have shown that there is a profound connection between information and entropy, a quantity that has been well accepted in science. Without this connection, information would be more difficult to apply to science. Two of the most important pillars in modern physics must be the Einstein's relativity theory and the Schrodinger's quantum mechanics. We show that there exists a profound relationship between them, by means of the uncertainty principle. In due of the uncertainty relation, we show that every bit of information takes time and energy to transfer, to create and to observe. Since one cannot create something from nothing, we show that, anything to be created needs a huge amount of energy and requires a great deal of entropy to make it happen! My question is that, can we afford it?

Schrödinger operators on half-line with shrinking potentials at the origin

We discuss the general model of a Schrodinger quantum particle constrained on a straight half-line with given self-adjoint boundary condition at the origin and an interaction potential supported around the origin. We study the limit when the range of the potential scales to zero and its magnitude blows up. We show that in the limit the dynamics is generated by a self-adjoint negative Laplacian on the half-line, with a possible preservation or modification of the boundary condition at the origin, depending on the magnitude of the scaling and of the strength of the potential.

Calibration and Simulation of Arbitrage Effects in a Non-Equilibrium Quantum Black-Scholes Model by Using Semi-Classical Methods

An non-equilibrium Black-Scholes model, where the usual constant interest rate r is replaced by a stochastic time dependent rate r(t) of the form r(t)=r+f (t)W(t), accounting for market imperfections and prices non-alignment, is developed. The white noise amplitude f (t), called arbitrage bubble, generates a time dependent potential U(t) which changes the usual equilibrium dynamics of the traditional Black-Scholes model. The purpose of this article is to tackle the inverse problem, that is, is it possible to extract the time dependent potential U(t) and its associated bubble shape f (t), from the real empirical financial data? In order to give an answer to this question, the interacting Black-Scholes equation must be interpreted as a quantum Schrodinger equation with Hamiltonian operator H=H0+ U(t), where H0 is the equilibrium Black-Scholes Hamiltonian and U(t) is the interaction term. By using semi-classical considerations and the knowledge about the mispricing of the financial data, one can determinate an approximate functional form of the potential term U(t) and its associated bubble f (t), In all the studied cases, the non-equilibrium model performs a better estimation of the real data than the usual equilibrium model. It is expected that this new and simple methodology could help to improve option pricing estimations.

Wave Function in Economics

In this research article: 1) the new quantum macroeconomics and microeconomics theories in the quantum econophysics science are formulated, 2) the notion on the wave function in the quantum macroeconomics and microeconomics theories in the quantum econophysics science is introduced, and 3) the quantum econophysical wave equations in the quantum macroeconomics and microeconomics theories in the quantum econophysics science are derived for the first time. Authors show that there is a certain conceptual scientific analogy between 1) the wave functions in the quantum econophysical wave equations in the quantum macroeconomics and microeconomics theories in the quantum econophysics science as well as 2) the wave function in the Schrodinger quantum mechanical wave equation in the quantum mechanics science. The wave function theories are created to make: 1) the economy’s state prediction at the certain time moment, using the wave function in the quantum econophysical wave equation in the quantum macroeconomic theory in the quantum econophysics science; and 2) the firm’s state prediction at the certain time moment, using the wave function in the quantum econophysical wave equation in the quantum microeconomic theory in the quantum econophysics science. Authors use the quantum econophysical wave equations in the quantum econophysics science to develop a new software program for the application by the central/commercial/investment banks with the purpose the make the accurate characterization and forecasting of: 1) the national/global economic performance changes, including the GIP((t), GDP(t), GNP(t) dependencies changes, in agreement with the quantum macroeconomics theory in the quantum econophysics science, and 2) the firm’s economic performance changes, including the EBITDA(t) dependence changes in agreement with the quantum microeconomics theory in the quantum econophysics science.

Identification problem of Klein–Gordon–Schrödinger quantum system control

Identification for Klein---Gordon---Schrodinger quantum control system as one of inverse problems is considered in this work. In particular, unknown parameters appeared at electric control field need to be identified as our target. The existence of optimal parameters is proved for quadratic criteria function. The profile of external control is recovered theoretically at the framework of variational method in complex Hilbert spaces.

A Fractal Menger Sponge Space-Time Proposal to Reconcile Measurements and Theoretical Predictions of Cosmic Dark Energy

The 95.5 percent of discrepancy between theoretical prediction based on Einstein’s theory of relativity and the accurate cosmological measurement of WMAP and various supernova analyses is resolved classically using Newtonian mechanics in conjunction with a fractal Menger sponge space proposal. The new energy equation is thus based on the familiar kinetic energy of Newtonian mechanics scaled classically by a ratio relating our familiar three dimensional space homology to that of a Menger sponge. The remarkable final result is an energy equation identical to that of Einstein’s E=mc2 but divided by 22 so that our new equation reads as . Consequently the energy Lorentz-like reduction factor of percent is in astonishing agreement with cosmological measurements which put the hypothetical dark energy including dark matter at percent of the total theoretical value. In other words our analysis confirms the cosmological data putting the total value of measured ordinary matter and ordinary energy of the entire universe at 4.5 percent. Thus ordinary positive energy which can be measured using conventional methods is the energy of the quantum particle modeled by the Zero set in five dimensions. Dark energy on the other hand is the absolute value of the negative energy of the quantum Schrodinger wave modeled by the empty set also in five dimensions.

Spectra of the quantized action variables of the compactified Ruijsenaars-Schneider system

A simple derivation of the spectra of the action-variables of the quantized compactified Ruijsenaars-Schneider system is presented. The spectra are obtained by combining Kahler quantization with the identification of the classical action-variables as a standard toric moment map on the complex projective space. The result is consistent with the Schrodinger quantization of the system worked out previously by van Diejen and Vinet.

Compound transfer matrices: Constructive and destructive interference

Scattering from a compound barrier, one composed of a number of distinct non-overlapping sub-barriers, has a number of interesting and subtle mathematical features. If one is scattering classical particles, where the wave aspects of the particle can be ignored, the transmission probability of the compound barrier is simply given by the product of the transmission probabilities of the individual sub-barriers. In contrast, if one is scattering waves (whether we are dealing with either purely classical waves or quantum Schrodinger wavefunctions) each sub-barrier contributes phase information (as well as a transmission probability), and these phases can lead to either constructive or destructive interference, with the transmission probability oscillating between nontrivial upper and lower bounds. In this article, we shall study these upper and lower bounds in some detail, and also derive bounds on the closely related process of quantum excitation (particle production) via parametric resonance.

Quantum equations from Brownian motions

Classical Schrodinger and Dirac equations have been derived from Brownian motions of a particle, it has been shown that the classical Schrodinger equation can be transformed to usual Schrodinger Quantum equation on applying Heisenberg uncertainty principle between position and momentum while Dirac Quantum equation follows from it’s classical counter part on applying Heisenberg uncertainty principle between energy and time without applying any analytical continuation.

Quantum Theory of Atom Laser Cooling

In this paper, we study the laser cooling mechanisms with extended Schrodinger quantum wave equation, which can describe a particle in conservative and non-conservative force field. We prove the atom in laser field can be cooled with the theory, and predict that the atom cooling temperature T is directly proportional to the atom vibration frequency ω, which are in accordance with experiment results (A.D. Oconnell, et al. in Nature 464:697, 2010).

Polymer quantization of the Einstein-Rosen wormhole throat

We present a polymer quantization of spherically symmetric Einstein gravity in which the polymerized variable is the area of the Einstein-Rosen wormhole throat. In the classical polymer theory, the singularity is replaced by a bounce at a radius that depends on the polymerization scale. In the polymer quantum theory, we show numerically that the area spectrum is evenly-spaced and in agreement with a Bohr-Sommerfeld semiclassical estimate, and this spectrum is not qualitatively sensitive to issues of factor ordering or boundary conditions except in the lowest few eigenvalues. In the limit of small polymerization scale we recover, within the numerical accuracy, the area spectrum obtained from a Schrodinger quantization of the wormhole throat dynamics. The prospects of recovering from the polymer throat theory a full quantum-corrected spacetime are discussed.

Theoretical Physics: A Primer for Philosophers of Science

We give a overview of the main areas in theoretical physics, with emphasis on their relation to Lagrangian formalism in classical mechanics. This review covers classical mechanics; the road from classical mechanics to Schrodinger's quantum mechanics; electromagnetism, special and general relativity, and (very briefly) gauge field theory and the Higgs mechanism. We shun mathematical rigor in favor of a straightforward presentation.

“Quantizations” of the second Painlevé equation and the problem of the equivalence of its L-A pairs

We show that the known Flaschka-Newell L-A pair for the second Painleve equation gives solutions to linear evolutionary equations similar to the quantum Schrodinger equations. Using the Fourier transform for distributions, we derive this pair from the classical Garnier pair.

Symmetry Transformation in Extended Phase Space: the Harmonic Oscillator in the Husimi Representation

In a previous work the concept of quantum potential is generalized into extended phase space (EPS) for a particle in linear and harmonic potentials. It was shown there that in contrast to the Schrodinger quantum mechanics by an appropriate extended canonical transformation one can obtain the Wigner representation of phase space quantum mecha- nics in which the quantum potential is removed from dynamical equation. In other words, one still has the form invariance of the ordinary Hamilton-Jacobi equation in this repre- sentation. The situation, mathematically, is similar to the disappearance of the centrifugal potential in going from the spherical to the Cartesian coordinates. Here we show that the Husimi representation is another possible representation where the quantum potential for the harmonic potential disappears and the modified Hamilton-Jacobi equation reduces to the familiar classical form. This happens when the parameter in the Husimi transformation assumes a specific value corresponding to Q-function.

Moment problem quantization within a generalized scalet-Wigner (auto-scaling) transform representation

For one-dimensional Schrodinger quantum systems, the correlation expression S(x, τ, a) ≡ Ψ*(x − τ/2/a)Ψ(x + τ/2) satisfies a fourth-order linear differential equation with regard to x. This generalizes the result previously derived by Handy (2001 J. Phys. A: Math. Gen. 34 L271), and Handy and Wang (2001 J. Phys. A: Math. Gen. 34 8297), with regard to S(x, 0, 1). We are then able to incorporate this within a generalized Wigner transform representation, through the use of scalets (Handy C R and Brooks H A 2001 J. Phys. A: Math. Gen. 34 3577). Energy quantization is achieved through a moment problem positivity analysis (focusing on the moments of the probability density, Ψ2) at a = 1, τ = 0. The wavefunction, Ψ, is then generated through a multiscale analysis proceeding from the unity scale, extended into the zero scale limit. The power moments, μp = ∫ dx xp Ψ(x), can be generated through a similar procedure. We present the general formalism and apply it to the (ix)3 potential.