A general form of the dynamical equations is obtained on the requirement of the superposition principle of quantum states; hence the constraint on the forms of the Lagrangians is acquired under an assumption of correspondence between state and field operator. It shows that the superposition principle requires the continuous transformation group of the Lagrangians to be compact, and that the Lag...

The development of computer languages or software artefacts from basic concepts to the final product is usually a process starting with an abstract model of a key concept and extending this by adding more detailed functionality for extended structural definitions. We will present a refinement approach for the stepwise development of algebraic models. In each step we either add new elements to a...

In quantum mechanics, any quantum state ‘vector’ | i may be expanded as a linear superposition of the eigenvectors of any Hermitian operator | i = P n an|ni. This is the Expansion Principle of quantum mechanics. For most problems, the Hermitian operator of choice is the Hamiltonian operator Ĥ = (p̂/2m0) + V (r), but it need not be. We choose the Hamiltonian operator since there exist a few probl...

According to Penrose, the fundamental conflict between the superposition principle of quantum mechanics and the principle of general covariance of general relativity entails the existence of wavefunction collapse, e.g. a quantum superposition of two different space-time geometries will collapse to one of them due to the ill-definedness of the time-translation operator for the superposition. In ...

This paper proposes a novel genetic quantum algorithm (GQA) to solve geometric constraint problems. Instead of binary, numeric or symbolic representation, we introduce qubit chromosome representation. GQA is based on qubit and superposition of states and is used in the process of geometric constraint solving in order to get the solution sequence. As GQA has diversity caused by the qubit represe...

In this paper, we obtained a necessary and sufficient condition for the embedding H?q([0,1])? IBVqp([0,1]), where IBVq p denotes set of functions bounded q-integral p-variation. Additionally, conditions composition superposition operators were provided to map space H?q([0,1]) into itself, by which these bounded. Finally, applied results examine existence uniqueness solutions Hammerstein integra...

Abstract We discuss the general matrix elements of squeezing operator between number eigenstates a harmonic oscillator (which may also represent quantized mode electromagnetic radiation). These have first been used by Popov and Perelomov (1969) long ago, in their thorough analysis parametric excitation oscillators. They expressed terms transcendental functions, associated Legendre functions. In...