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Nonlinear Boundaries in Quantum Mechanics     Nonlinear Boundaries  Quantum Mechanics  Quantum Physics       font style='font-size:12px;'> 2011/7/28
Abstract: Based on empirical evidence, quantum eigenvalue equations appear to be strictly linear and gauge invariant. This work uses concise mathematics to show that quantum eigenvalue equations on a ...
Abstract: The Schroedinger equation is up-to-a-phase invariant under the Galilei group. This phase leads to the Bargmann's superselection rule, which forbids the existence of the superposition of stat...
The aim of the article is to argue that the interpretations of quantum mechanics and of probability are much closer than usually thought. Indeed, a detailed analysis of the concept of probability (wit...
We review our approach to quantum mechanics adding also some new interesting results. We start by giving proof of two important theorems ms on the existence of the A(Si) and i,±1 N Clifford algebras. ...
We explore a new simple N = 2 SQM model describing the motion over complex manifolds in external gauge fields. The nilpotent supercharge Q of the model can be interpreted as a (twisted) exterior holom...
Riemann hypothesis and Quantum Mechanics      Bost-Connes model  Riemann Hypothesis  Primorial numbers       font style='font-size:12px;'> 2011/2/24
In their 1995 paper, Jean-Benoˆıt Bost and Alain Connes (BC) constructed a quantum dynamical system whose partition function is the Riemann zeta function ζ(β),where β is an inverse temperatu...
We study the phase diagram of scalar field theory on a three dimensional Euclidean spacetime whose spatial component is a fuzzy sphere. The corresponding model is an ordinary one-dimensional matrix mo...
A Closed Formula for the Barrier Transmission Coefficient in Quaternionic Quantum mechanics.
It will be seen that the determination of general one-dimensional Schr¨odinger Hamiltonians having third-order differential ladder operators requires to solve the Painlev´e IV equation. It shall...
Riemann hypothesis and Quantum Mechanics      Bost-Connes model  Riemann Hypothesis  Primorial numbers       font style='font-size:12px;'> 2011/3/4
In their 1995 paper, Jean-Benoˆıt Bost and Alain Connes (BC) constructed a quantum dynamical system whose partition function is the Riemann zeta function ζ(β),where β is an inverse temperatu...
The many-body space fractional quantum system is studied using the density matrix method. We give the new results of the Thomas-Fermi model, and obtain the quantum pressure of the free electron gas. W...
DNA Sequencing via Quantum Mechanics and Machine Learning     DNA Sequencing  Quantum Mechanics  Machine Learning       font style='font-size:12px;'> 2011/1/5
Rapid sequencing of individual human genome is prerequisite to genomic medicine, where diseases will be prevented by preemptive cures. Quantum-mechanical tunneling through single-stranded DNA in a sol...
In this work, we study the existence and the uniqueness and the regularity of the solution of a problem governed by a nonlinear equation intervening in relativistic quantum mechanics perturbed by an a...
We discuss two independent constructions to introduce an N-extended Super-symmetric Quantum Mechanics. The first one makes use of the Fierz identities while the second one (divided into two subcases) ...
The general aim of this paper is to extend the Modal-Hamiltonian interpretation of quantum mechanics to the case of relativistic quantum mechanics with gauge U(1) fields.

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