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Replication of DNA and synthesis of proteins are studied from the view-point of quantum database search. Identification of a base-pairing with a quantum query gives a natural (and first ever!) explanation of why living organisms have 4 nucleotide bases and 20 amino acids. It is amazing that these numbers arise as solutions to an optimisation problem. Components of the DNA structure which implement...
The dynamics of a particle which is linearly coupled to a boson field is investigated. The boson field induces superselection rules for the momentum of the particle, if the field is infrared divergent. Thereby the Hamiltonian of the total system remains bounded from below.
We consider the modification of a single-particle Schrödinger equation by the inclusion of an additional gravitational self-potential term which follows from the prescription that the ‘massdensity’ that enters this term is given by m|ψ( $$\overrightarrow r $$ ,t)|2, where ψ( $$\overrightarrow r $$ ,t) is the wave function and m is the mass of the particle. This leads to a nonlinear equation,...
On the face of some recent experiments claiming the simultaneous presence of both ‘sharp interference’ and ‘highly reliable which way information’ and some others casting light on the origin of complementarity in quantum interferometric experiments, the whole issue is reviewed on the basis of our earlier precise formulation of Bohr’s complementarity principle. It is pointed out that contradicting...
One of the simplest examples of a $$ \mathcal{P}\mathcal{T} $$ -symmetric quantum system is the scaling Yang-Lee model, a quantum field theory with cubic interaction and purely imaginary coupling. We give a historical review of some facts about this model in d ≤ 2 dimensions, from its original definition in connection with phase transitions in the Ising model and its relevance to polymer physics,...
The topics of confinement, average forces, and the Ehrenfest theorem are examined for a particle in one spatial dimension. Two specific cases are considered: (i) A free particle moving on the entire real line, which is then permanently confined to a line segment or ‘a box’ (this situation is achieved by taking the limit V0 → ∞ in a finite well potential). This case is called ‘a particle-in-an-infinite-square-well-potential’...
We examine the dynamical evolution of wave packets in a cubical billiard where three quantum numbers (nx, ny, nz) determine its energy spectrum and consequently its dynamical behaviour. We have constructed the wave packet in the cubical billiard and have observed its time evolution for various...
We present an alternative formalism of quantum mechanics tailored to statistical ensemble in phase space. The purpose of our work is to show that it is possible to establish an alternative autonomous formalism of quantum mechanics in phase space using statistical methodology. The adopted perspective leads to obtaining within the framework of its theory the fundamental quantum-mechanical equation without...
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