Related papers: Comment on the uncertainty relation with periodic …
Heisenberg-Robertson's uncertainty relation expresses a limitation in the possible preparations of the system by giving a lower bound to the product of the variances of two observables in terms of their commutator. Notably, it does not…
Coherence of a quantum state intrinsically depends on the choice of the reference basis. A natural question to ask is the following: if we use two or more incompatible reference bases, can~there be some trade-off relation between the…
Quantum dynamics of a particle confined in a box with time-dependent wall is revisited by considering some unexplored aspects of the problem. In particular, the case of dynamical confinement in a time-dependent box in the presence of purely…
We study the commutation relations, uncertainty relations and spectra of position and momentum operators within the framework of quantum group % symmetric Heisenberg algebras and their (Bargmann-) Fock representations. As an effect of the…
One of the main interest in quantum cosmology is to determine boundary conditions for the wave function of the universe which can predict observational data of our universe. For this purpose, we solve the Wheeler-DeWitt equation for a…
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…
The dynamics of a light fermion bound to a heavy one is expected to be described by the Dirac equation with an external potential. The potential breaks translation invariance, whereas the bound state momentum is well defined. Boosting the…
Various theories that aim at unifying gravity with quantum mechanics suggest modifications of the Heisenberg algebra for position and momentum. From the perspective of quantum mechanics, such modifications lead to new uncertainty relations…
We have used different methods to obtain the bound states of a Hamiltonian of a relativistic two scalar particle system in a local potential. The potentials we are interested in are binding and confining potentials, that are associated with…
Uncertainty relations are one of the fundamental principles in physics. It began as a fundamental limitation in quantum mechanics, and today the word {\it uncertainty relation} is a generic term for various trade-off relations in nature. In…
Heisenberg's uncertainty principle is formulated for a set of generalized measurements within the framework of majorization theory, resulting in a partial uncertainty order on probability vectors that is stronger than those based on…
In the preceding Comment (quant-ph/0209032) Trifonov disputes our recently proposed uncertainty relations for a quantum particle on a circle. He states that (i) the quantity $\Delta^2(\hat\phi)$ introduced by us representing the uncertainty…
The exact two-particle energy eigenstates in an asymmetric rectangular box with periodic boundary conditions in all three directions are studied. Their relation with the elastic scattering phases of the two particles in the continuum are…
We introduce a geometric formulation of quantum indeterminacy from which the standard uncertainty inequalities emerge as necessary consequences. Our approach is based on convex geometry in phase space and on methods from symplectic…
The complexity of the quantum state of a multiparticle system and the maximum possible accuracy of its quantum description are connected by a relation similar to the coordinate-momentum uncertainty relation. The coefficient in this relation…
We show how the state of an unstable particle can be defined in terms of stable asymptotic states. This general definition is used to discuss and to solve some old problems connected with the short-time and large-time behaviour of the…
It is shown that a choice of degrees of freedom of a bipartite continuous variable system determines amount of non-classical correlations (quantified by discord) in the system's state. Non-classical correlations (that include entanglement…
The Heisenberg position-momentum uncertainty relation is a cornerstone of quantum mechanics. However, its standard formulation is not fully consistent with special relativity. While partial understanding has been achieved in the…
The uncertainty relations for the position and momentum of a quantum particle on a circle are identified minimized by the corresponding coherent states. The sqeezed states in the case of the circular motion are introduced and discussed in…
We study the behavior of a quantum particle trapped in a confining potential in one dimension under multiple sudden changes of velocity and/or acceleration. We develop the appropriate formalism to deal with such situation and we use it to…