相关论文: Complementarity of representations in quantum mech…
In this note we show that the momentum and position operators of $\mu$-deformed quantum mechanics for $\mu > 0$ are not Accardi complementary in a sense that we will define. We conjecture that this is also true if $-1/2 < \mu < 0$.
One of the key conceptual challenges in quantum gravity is to understand how quantum theory should modify the very notion of spacetime. One way to investigate this question is to study the alternatives to Schr\"odinger quantum mechanics.…
Niels Bohr introduced the concept of complementarity in order to give a general account of quantum mechanics, however he stressed that the idea of complementarity is related to the general dificulty in the formation of human ideas, inherent…
We review the notion of complementarity of observables in quantum mechanics, as formulated and studied by Paul Busch and his colleagues over the years. In addition, we provide further clarification on the operational meaning of the concept,…
A quantum mechanics representation based on position ($\vec{r}$), linear momentum($\vec{p}$) and energy($E$) eigenvalues is presented here. A set of equations, explicitly independent on wave function, was derived relating these observables.…
Earlier work on modular arithmetic of k-ary representations of length L of the natural numbers in quantum mechanics is extended here to k-ary representations of all natural numbers, and to integers and rational numbers. Since the length L…
A representation theorem for non-semibounded Hermitian quadratic forms in terms of a (non-semibounded) self-adjoint operator is proven. The main assumptions are closability of the Hermitian quadratic form, the direct integral structure of…
We show (an earlier conjecture of the last two authors) that the momentum and position operators of mu-deformed quantum mechanics for -1/2 < mu < 0 are not Accardi complementary. We also prove some related formulas that were conjectured by…
Bohr's principle of complementarity lies at the central place of quantum mechanics, according to which the light is chosen to behave as a wave or particles, depending on some exclusive detecting devices. Later, intermediate cases are found,…
The trajectory representation in the high energy limit (Bohr correspondence principle) manifests a residual indeterminacy. This indeterminacy is compared to the indeterminacy found in the classical limit (Planck's constant to 0) [Int. J.…
Quantizing the transfer of energy and momentum between interacting particles, we obtain a quantum impulse equation and relations that the corresponding mechanical power, force and torque satisfy. In addition to the energy-frequency and…
We give two simple Kochen-Specker arguments for complementary between the position and momentum components of spinless particles, arguments that are identical in structure to those given by Peres and Mermin for spin-1/2 particles.
We re-derive the Schr\"{o}dinger-Robertson uncertainty principle for the position and momentum of a quantum particle. Our derivation does not directly employ commutation relations, but works by reduction to an eigenvalue problem related to…
The Copenhagen interpretation of quantum mechanics, which first took shape in Bohr's landmark 1928 paper on complementarity, remains an enigma. Although many physicists are skeptical about the necessity of Bohr's philosophical conclusions,…
There is presented a contextual statistical model of the probabilistic description of physical reality. Here contexts (complexes of physical conditions) are considered as basic elements of reality. There is discussed the relation with QM.…
We study some fundamental issues related to the Hilbert space representation of quantum mechanics in the presence of a minimal length and maximal momentum. In this framework, the maximally localized states and quasi-position representation…
Kirkwood-Dirac representations of quantum states are increasingly finding use in many areas within quantum theory. Usually, representations of this sort are only applied to provide a representation of quantum states (as complex functions…
We formulate quantum mechanics in the two-dimensional torus without using position operators. We define an algebra with only momentum operators and shift operators and construct irreducible representation of the algebra. We show that it…
In this paper we undertake an analysis of the eigenstates of two non self-adjoint operators $\hat q$ and $\hat p$ similar, in a suitable sense, to the self-adjoint position and momentum operators $\hat q_0$ and $\hat p_0$ usually adopted in…
Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert…