321 citations · 465 across the 16 of their papers we have counts for
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On momentum operators given by Killing vectors whose integral curves are geodesics
Thomas Schürmann
We consider momentum operators on intrinsically curved manifolds. Given that the momentum operators are Killing vector fields whose integral curves are geodesics, it is shown that…
The uncertainty principle in terms of isoperimetric inequalities
Thomas Schürmann
Simultaneous measurements of position and momentum are considered in dimensions. We find, that for a particle whose position is strictly localized in a compact domain $D\subset…
A note on entropic uncertainty relations of position and momentum
Thomas Schürmann
We consider two entropic uncertainty relations of position and momentum recently discussed in literature. By a suitable rescaling of one of them, we obtain a smooth interpolation o…
Single-slit diffraction and the Heisenberg principle for position and momentum
W. Görlich, I. Hoffmann, T. Schürmann
Monochromatic light is prepared by a single slit of spatial width Δx. The diffraction pattern is considered to obtain the corresponding probability density of the momentum. Let P b…
On the measurement probability of quantum phases
Thomas Schürmann
We consider the probability by which quantum phase measurements of a given precision can be done successfully. The least upper bound of this probability is derived and the associat…
A single particle uncertainty relation
Thomas Schürmann
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 previou…