Related papers: Another look through Heisenberg's microscope
In the history of quantum mechanics, various types of uncertainty relationships have been introduced to accommodate different operational meanings of Heisenberg uncertainty principle. We derive an optimized entropic uncertainty relation…
Although Heisenberg's uncertainty principle is represented by a rigorously proven relation about intrinsic indeterminacy in quantum states, Heisenberg's error-disturbance relation (EDR) has been commonly believed as another aspect of the…
The Schrodinger equation is incomplete, inherently unable to explain the collapse of the wavefunction caused by measurement; a fundamental issue known as the quantum measurement problem. Quantum mechanics is generally constrained by the…
We address the problem of interference using the Heisenberg picture and highlight some new aspects through the use of pre-selection, post-selection, weak measurements, and modular variables, We present a physical explanation for the…
An effective formalism is developed to handle decaying two-state systems. Herewith, observables of such systems can be described by a single operator in the Heisenberg picture. This allows for using the usual framework in quantum…
Uncertainty relations (URs) like the Heisenberg-Robertson or the time-energy UR are often considered to be hallmarks of quantum theory. Here, a simple derivation of these URs is presented based on a single classical inequality from…
The problem of a correct description of the physical phenomena of the Heisenberg uncertainty relation is solved by using a variable hidden in Newtonian mehcanics.
Heisenberg's uncertainty principle was originally formulated in 1927 as a quantitative relation between the "mean error" of a measurement of one observable and the disturbance thereby caused on another observable. Heisenberg derived this…
It is generally accepted that the disturbance interpretation cannot explain Heisenberg's uncertainty relation DxDp=h. In this paper a clear distinction will be made between the notions of state preparation and measurement, noting that the…
We study the formulation of the uncertainty principle in quantum mechanics in terms of entropic inequalities, extending results recently derived by Bialynicki-Birula [1] and Zozor et al. [2]. Those inequalities can be considered as…
One of the formulations of Heisenberg uncertainty principle, concerning so-called measurement uncertainty, states that the measurement of one observable modifies the statistics of the other. Here, we derive such a measurement uncertainty…
Relaxing the postulates of an axiomatic theory is a natural way to find more general theories, and historically, the discovery of non-Euclidean geometry is a famous example of this procedure. Here, we use this way to extend quantum…
The Heisenberg microscope provides a powerful mental image of the measurement process of quantum mechanics (QM), attempting to explain the uncertainty relation through an uncontrollable back-action from the measurement device. However,…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
For a quantum particle with a single degree of freedom, we derive preparational sum and product uncertainty relations satisfied by $N$ linear combinations of position and momentum observables. The state-independent bounds depend on their…
The second law of thermodynamics states that entropy increases (or does not change) by time in an isolated system. As microscopic physical laws are reversible, the origin of irreversibility is not straightforward. Although the outcome of a…
The original Schrodinger's paper is translated and annotated in honour of the 70-th anniversary of his Uncertainty Relation [published also in: Bulg. Journal of Physics,vol.26,no.5/6 (1999) pp.193-203]. In the annotation it is shown that…
The uncertainty relation of three quantities in quantum mechanics is estimated in terms of commutators. The Pauli matrices are used to find a contribution of third-order commutators. The resulting inequality refines the Heisenberg…
We consider successive measurements of position and momentum of a single particle. Let P be the conditional probability to measure the momentum k with precision dk, given a previously successful position measurement q with precision dq.…
The $D$-dimensional harmonic system (i.e., a particle moving under the action of a quadratic potential) is, together with the hydrogenic system, the main prototype of the physics of multidimensional quantum systems. In this work we…