A Computational Model for Observation in Quantum Mechanics

A computational model of observation in quantum mechanics is presented. The model provides a clean and simple computational paradigm which can be used to illustrate and possibly explain some of the unintuitive and unexpected behavior of some quantum mechanical systems. As examples, the model is used to simulate three seminal quantum mechanical experiments. The results obtained agree with the predictions of quantum mechanics (and physical measurements), yet the model is perfectly deterministic and maintains a notion of locality.

Java Applets for teaching quantum mechanics: Particle in a box

These Java Applets help to illustrate some of the difficult to grasp concepts of quantum mechanics. To run this Applet, use the 'Download as zip files' option. Make sure you extract the files first, then double click on the .html file to run the Applet. These are released as open access resources for the purpose of testing, and are to be deployed at the users own risk. Please report any errors you find.

Java Applets for teaching quantum mechanics: Particle in a 2D box

These Java Applets help to illustrate some of the difficult to grasp concepts of quantum mechanics. To run this Applet, use the 'Download as zip files' option. Make sure you extract the files first, then double click on the .html file to run the Applet. These are released as open access resources for the purpose of testing, and are to be deployed at the users own risk.

Java Applets for teaching quantum mechanics: Particle in a well

These Java Applets help to illustrate some of the difficult to grasp concepts of quantum mechanics. To run this Applet, use the 'Download as zip files' option. Make sure you extract the files first, then double click on the .html file to run the Applet. These are released as open access resources for the purpose of testing, and are to be deployed at the users own risk.

Quantum mechanics studies of the tautomers of dlhydrodiacetylformoin, an important Maillard intermediate and the synthesis of furaneol

Conformational analyses have been carried out on the acyclic and cyclic forms of dihydrodiacetylformoin, an important Maillard intermediate and precursor for furaneol. For the acyclic forms, the 2,5-dicarbonyl isomers have the lowest energy, while for the cyclic forms, the 3-carbonyl are favoured over the 4-carbonyl isomers. The likely path for cyclisation is investigated and it is shown that the favoured path is dependent upon the relative chiralities of the carbon atoms and in particular that the reaction proceeds more readily if C2 and C3 have different chiralities. After cyclisation, the reaction path to produce furaneol proceeds via the loss of a water molecule. This reaction has been studied with a model including two water molecules and a hydroxide anion and shows relatively low-energy barriers. (C) 2008 Published by Elsevier B.V.

Quantum mechanics studies of the tautomers of diacetylformoin, an important maillard product and odorant

Diacetylformoin (3,4-dihydroxy-3-hexene-2,5-dione) has 16 tautomers, many with several possible conformations and all have been geometry optimised using quantum mechanics at the HF/6-31+G* level. Eleven structures have been identified with energies within 10 kcal mol(-1) of the minimum energy structure. Of these eight are acyclic and three cyclic. Calculations of NMR spectra have clarified the identity of the acyclic and cyclic structures found experimentally. The mechanism for cyclisation has been investigated and transition states obtained. The lowest energy reaction path requires the loss and gain of a proton during cyclisation. (c) 2006 Elsevier B.V. All rights reserved.

Path integral representations in noncommutative quantum mechanics and noncommutative version of Berezin-Marinov action

It is known that the actions of field theories on a noncommutative space-time can be written as some modified (we call them theta-modified) classical actions already on the commutative space-time (introducing a star product). Then the quantization of such modified actions reproduces both space-time noncommutativity and the usual quantum mechanical features of the corresponding field theory. In the present article, we discuss the problem of constructing theta-modified actions for relativistic QM. We construct such actions for relativistic spinless and spinning particles. The key idea is to extract theta-modified actions of the relativistic particles from path-integral representations of the corresponding noncommutative field theory propagators. We consider the Klein-Gordon and Dirac equations for the causal propagators in such theories. Then we construct for the propagators path-integral representations. Effective actions in such representations we treat as theta-modified actions of the relativistic particles. To confirm the interpretation, we canonically quantize these actions. Thus, we obtain the Klein-Gordon and Dirac equations in the noncommutative field theories. The theta-modified action of the relativistic spinning particle is just a generalization of the Berezin-Marinov pseudoclassical action for the noncommutative case.

Orthogonality criterion for banishing hydrino states from standard quantum mechanics

Orthogonality criterion is used to show in a very simple and general way that anomalous bound-state solutions for the Coulomb potential (hydrino states) do not exist as bona fide solutions of the Schrodinger, Klein-Gordon and Dirac equations. (C) 2007 Elsevier B.V. All rights reserved.

Nonlinear Lattice Within Supersymmetric Quantum Mechanics Formalism

In the last decades, the study of nonlinear one dimensional lattices has attracted much attention of the scientific community. One of these lattices is related to a simplified model for the DNA molecule, allowing to recover experimental results, such as the denaturation of DNA double helix. Inspired by this model we construct a Hamiltonian for a reflectionless potential through the Supersymmetric Quantum Mechanics formalism, SQM. Thermodynamical properties of such one dimensional lattice are evaluated aming possible biological applications.

Zel'dovich's method of perturbation theory in quantum mechanics

Many years ago Zel'dovich showed how the Lagrange condition in the theory of differential equations can be utilized in the perturbation theory of quantum mechanics. Zel'dovich's method enables us to circumvent the summation over intermediate states. As compared with other similar methods, in particular the logarithmic perturbation expansion method, we emphasize that this relatively unknown method of Zel'dovich has a remarkable advantage in dealing with excited stares. That is, the ground and excited states can all be treated in the same way. The nodes of the unperturbed wavefunction do not give rise to any complication.

Time-reversal aspect of the point interactions in one-dimensional quantum mechanics

It is known that there is a four-parameter family of point interactions in one-dimensional quantum mechanics. We point out that, as far as physics is concerned, it is sufficient to use three of the four parameters. The fourth parameter is redundant. The apparent violation of time-reversal invariance in the presence of the fourth parameter is an artifact.

Renormalization group invariance of quantum mechanics

We propose a framework to renormalize the nonrelativistic quantum mechanics with arbitrary singular interactions. The scattering equation is written to have one or more subtraction in the kernel at a given energy scale. The scattering amplitude is the solution of a nth order derivative equation in respect to the renormalization scale, which is the nonrelativistic counterpart of the Callan-Symanzik formalism, Scaled running potentials for the subtracted equations keep the physics invariant fur a sliding subtraction point. An example of a singular potential, that requires more than one subtraction to renormalize the theory is shown. (C) 2000 Published by Elsevier B.V. B.V. All rights reserved.