If one begins with a system in a precisely known quantum state, then unitary evolution guarantees that the details about that system will evolve in such a way that one can infer the precise quantum state of the system at some later time (as long as one knows the law of evolution and can perform the relevant calculations), and vice versa.
This approach has been applied to various applications, such as chemical sensing, dimensional crossover influence in granular electronic systems, heterojunction tunneling field effect transistors, and precise quantum dot placement [2 6].
This argument is not precise enough to prove that the resultant force is attractive, but an exact quantum mechanical calculation shows that it is if the protons are not too close together.
One may mention many-valued, or multivalued, logics, which admit a finite number of truth-values; fuzzy logic, with an imprecise membership relationship (though, paradoxically, a precise equality relation); and quantum logic, where conjunction may be only partially defined and implication may not be defined at all.
Many of these technologies rely on an optical probe, either coherent or squeezed states to make a precise measurement of a parameter ultimately limited by quantum mechanics.
The integration of semiconductor quantum dots (QD) as active elements in new quantum optoelectronic devices [1 4] requires a precise control in their shape, size and location over the substrate.
Shortcuts are also relevant to clarify fundamental questions such as a precise quantification of the third principle of thermodynamics and quantum speed limits.
One advantage of determining the fluorescence in real time is a precise determination of the decay time for the molecular quantum mechanical transition, which is responsible for light emission.
With the advent of quantum mechanics and the Schrödinger equation in the 1920s, atomic theory became a precise mathematical science.
See his paper for a precise formulation and Strocchi (2008) for a thorough and rigorous treatment of symmetry breaking in classical and quantum physics.
