Seminár Katedry teoretickej fyziky - Konrad Szymański (28.4.2026)

v utorok 28.4.2026 o 14:00 hod. v miestnosti F2/125

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Prednášajúci: Konrad Szymański (RCQI FÚ SAV)

Názov: Geometry of expectation values of non-commuting observables

Termín: 28.4.2026, 14:00 hod., miestnosť F2 125

Abstrakt:
Quantum-mechanical expectation values have a simple definition, analogous to the one in standard probability theory: a sum of values weighted by the probabilities of observing each outcome. Naturally, the expectation value is a function of state; and if several observables X₁,...,X_k are measured, to each state there corresponds a vector (⟨X₁⟩,...,⟨X_k⟩) of expectation values. Considering the set of all such vectors, taken over all quantum states, leads naturally to the study of their geometry; these sets are known as numerical ranges. Their geometric properties reveal peculiar features of quantum mechanics; in particular, the fact that the underlying probabilities cannot arise from a classical random process. In this talk I will give an elementary introduction to the geometry of numerical ranges, present examples for simple quantum-mechanical systems, and show how uncertainty relations can be understood through the lens of this formalism

 

 

 

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