Quantum Mechanics

A pedagogical review on supersymmetry in quantum mechanis is presented which provides a comprehensive coverage of the subject. First, the key ingredients on the quantization of the systems with anticommuting variables are discussed. The supersymmetric Hamiltotian in quantum mechanics is then constructed by emphasizing the role of partner potentials and the superpotentials. We also make explicit the mathematical formulation of the Hamiltonian by considering in detail the N=1 and N=2 supersymmetric (quantum) mechanics. Supersymmetry is then discussed in the context of one-dimensional problems and the importance of the factorization method is highlighted. We treat in detail the technique of constructing a hierarchy of Hamiltonians employing the so-called ‘shape-invariance’ of potentials. To make transparent the relationship between supersymmetry and solvable potentials, we also solve several examples. We then go over to the formulation of supersymmetry in radial problems, paying a spec...

Part I – Spirilla Theory and Cosmology
Stephen Hawking once proclaimed that String Theory may be able to unify the various forces although later he became disillusioned thinking that there may be no Theory of Everything. This very condensed book pulls together the various forces into the Spirilla Theory which supersedes String Theory and introduces the Relativity of Consciousness.

The foundation of the Spirilla Theory is based on the writings of H. P. Blavatsky, A. B. Bailey, and A. Besant. By overlaying the works of Einstein, Bohm, de Broglie, Dirac, Bell and other great scientific minds, on top of the foundation, the unification of the various forces and theories starts to appear; each field of study supplying a part of the puzzle but only a holistic view of ALL endeavors will solve the mystery. The book starts by laying the groundwork through the Introduction, a review of Bell’s Theorem and p-adic mathematics; following this, each major section begins with a quote from the foundational works followed by the quotes from scientific papers demonstrating the current known thinking on the various topics; no attempts are made to edit the works (except with a few exceptions for clarity and/or length) of the various authors and references to the scientists’ works are maintained. Each section is pulled together so that a picture can be seen.
This section;
1. Redefines the atom with the addition of a subquark;
2. Defines the Spirilla Theory which unifies Quantum Mechanics and General Relativity, and explains Quantum Entanglement;
3. Defines new particles;
4. Redefines time and space;
5. Defines and solves the mystery of Black Holes and links the cosmic and quantum black hole through the spirillae;
6. Delves into the mystery of the Macroverse;
7. Outlines the steps in the origins of the universe;
8. Adds an equation to Einstein’s original 1905 paper on relativity which sees the speed of light approaching infinity;
9. Gives the foundation for developing space travel; and, as an appendix,
10. Gives detailed information for the development of a new energy source – Quantum Energy.

Part II - Ontology, Epistemology & Manifestations
Part II is divided into three sections:
1. Ontology and the fundamental concepts of reality which discusses:
a. consciousness and delves into the mystery of human consciousness having cosmic origins;
b. reincarnation and gives the various laws affecting rebirth, with a discussion on the principle of mutation and the perfecting of form;
c. the work of form-building, transmutation of form and the building of a human form.
2. Epistemology which covers a great deal of topics however; for the purposes of NOE the subject is restricted to;
a. evolution including a definition of the Law of Evolution, the cyclic ebb and flow and the rhythmic work of creation, the process of substitution, the evolution of man and the genesis of the pithecoid stocks; and
b. death including the processes of death, two main reasons for cremation and the sequence of events at death.
3. Manifestations of the various religions including:
a. why Christians don’t believe in reincarnation;
b. the coming science of invocation and evocation;
c. Quantum Entanglement Over Time (QEoT) or The Law of Cause and Effect, and The Law of Karma with a discussion on The Golden Rule ; and
d. The New World Religion.

The charged quantum geometry of mass-ENERGY-Matter - developed from the foundational postulate that quantised angular momenta of Planck's constant is in fact reflective of an equilateral mass-energy geometry from which all 2d immaterial EM fields and 3D material particles are created.

A generalization of the differential geometry of forms and vector fields to the case of quantum Lie algebras is given. In an abstract formulation that incorporates many existing examples of differential geometry on quantum spaces we combine an exterior derivative, in-ner ...

Salicylate synthase from Mycobacterium tuberculosis, MbtI, initiates the biosynthesis of siderophores by converting chorismate to salicylate. Nevertheless, three more distinct activities for wild-type MbtI have been detected in vitro: isochorismate synthase, isochorismate pyruvate lyase, and chorismate mutase. In this work, hybrid Quantum Mechanics/Molecular Mechanics methods have been used to get the first simulation of the chorismate mutase activity of MbtI.

We present a physical example model of how Quantum Control with genetic algorithms is applied to implement the quantum superdense code protocol. We studied a model consisting of two quantum dots with an electron with spin, including spin-orbit interaction. The electron and the spin get hybridized with the site acquiring two degrees of freedom, spin and charge. The system has tunneling and site energies as time dependent control parameters that are optimized by means of genetic algorithms to prepare a hybrid Bell-like state used as a transmission channel. This state is transformed to obtain any state of the four Bell basis as required by superdende protocol to transmit two bits of classical information. The control process protocol is equivalent to implement one of the quantum gates X, Z ʹ in the charge subsystem. Fidelities larger than 99.5 % are achieved for the hybrid entangled state preparation and the superdense operations.

My research question is “Does Belinfante’s argument that physical nature is pervaded by consciousness, as suggested by consciousness-base theory, prove the existence of God?” I started off my research by reading scientific books on Quantum Mechanics where I came across Belinfante’s argument. It holds the view that the weird behaviors of the sub-atomic particles (SAP) imply the existence of a being like God. I first explored the logic behind his argument, and identified one of the main assumption made by Belinfante; that consciousness is non-physical. So I introduced the studies of John Eccles and Karl Popper, which support the assumption and further explain, using Quantum Mechanics, how God controls the SAPs. I then brought in Dennett’s argument of consciousness being an illusion because it can be replicated with programming, which doesn’t affect Belinfante’s argument much. The next aspect is on whether the being implied by the behaviors of SAPs is actually God, leading me to compare it with St Aquinas’s description of what God is; It fulfilled most of the ‘criteria’ of what makes a being God.  I then explored whether Quantum Mechanics itself is in disagreement with God’s existence because of its probabilistic nature. If we adapt Subjective Bayesianism to probability, it turns out to support God’s existence instead. I then evaluated the relationship between science and religion, on whether they are in harmony or disagreement- in many cases, they actually rely on each other extensively. Finally, I moved on to consider the claims by Buddhists that reasoning alone cannot prove the existence of God because the act of thinking is contaminated with subjective opinion. I concluded by saying Belinfante’s argument strongly support the existence of God, perhaps not to the extent that it proves it, but enough to heavily impact our belief.

Quantum mechanics has revolutionized the way we view the physical world. This theory has required a dramatic revision in the structure of the laws of mechanics governing the behavior of the particles and lead to the discovery of macroscopic quantum e¤ects ranging from lasers and superconductivity to neutron stars and radiation from black holes. Though its validity is well con…rmed by the experimental evidence available, quantum mechanics remains somewhat of a mystery. The purpose of this study is to identify students’conceptual and mathematical di¢ culties in learning the core concepts of introductory quantum mechanics, with the eventual goal of developing instructional material to help students with these di¢ culties. We have investigated student understanding of several core topics in the introductory courses, including quantum measurement, probability, Uncertainty Principle, wave functions, energy eigenstates, recognizing symmetry in physical systems, and mathematical formalism. ...

In this paper, I present a mapping between representation of some quantum phenomena in one dimension and behavior of a classical time-dependent harmonic oscillator. For the first time, it is demonstrated that quantum tunneling can be described in terms of classical physics without invoking violations of the energy conservation law at any time instance. A formula is presented that generates a wide class of potential barrier shapes with the desirable reflection (transmission) coefficient and transmission phase shift along with the corresponding exact solutions of the time-independent Schr\"odinger's equation. These results, with support from numerical simulations, strongly suggest that two uncoupled classical harmonic oscillators, which initially have a 90\degree relative phase shift and then are simultaneously disturbed by the same parametric perturbation of a finite duration, manifest behavior which can be mapped to that of a single quantum particle, with classical 'ran...

The open electron resonator, described by Duncan et al. [D.S. Duncan, M.A. Topinka, R.M. Westervelt, K.D. Maranowski, A.C. Gossard, Phys. Rev. B 64 (2001) 033310. [1]], is a mesoscopic device that has attracted considerable attention due to its remarkable behaviour (conductance oscillations), which has been explained by detailed theories based on the behaviour of electrons at the top of the Fermi sea. In this work, we study the resonator using the simple quantum quantum electrical circuit approach, developed recently by Li and Chen [Y.Q. Li, B. Chen, Phys. Rev. B 53 (1996) 4027. [2]]. With this approach, and considering a very simple capacitor-like model of the system, we are able to theoretically reproduce the observed conductance oscillations. A very remarkable feature of the simple theory developed here is the fact that the predictions depend mostly on very general facts, namely, the discrete nature of electric charge and quantum mechanics; other detailed features of the systems described enter as parameters of the system, such as capacities and inductances.

Cabibbo-suppressed charm decays offer a good laboratory for studying weak interactions as they provide a unique window on the physics governing the decay-rate dynamics and CP violation. The branching ratios of the singly Cabibbo-suppressed decays of D0 meson are anomalous since the branching fraction of D0! m mÿ is observed to be suppressed relative to that of D0! K Kÿ by a factor of almost three [1], even though the phase space for the former is larger. The branching ratios of three-body decays of the D0 [2, 3] have larger uncertainties ...

Under the common viewpoint of statistical maps,the concept of observables in quantum mechanics and inclassical probability theory are discussed and compared.It is shown that, by means of injective statistical maps, quantum mechanics can to a certain extentbe reformulated in classical terms. Some characteristicexamples are considered.