Quaternionic Heisenberg-Robertson-Schrodinger and Maccone-Pati Uncertainty Principles
Let $\mathcal{Q}$ be a quaternionic Hilbert space. Let $A: \mathcal{D}(A)\subseteq \mathcal{Q}\to \mathcal{Q}$ and $B:\mathcal{D}(B)\subseteq \mathcal{Q}\to \mathcal{Q}$ be possibly unbounded self-adjoint linear operators. Then for all $h \in \mathcal{D}(AB)\cap \mathcal{D}(BA)$ with $\|h\|=1$, we show that \begin{align*} (1) \quad \quad \quad \Delta _h(A)\Delta _h(B)\geq \frac{\sqrt{|\langle \{A,B\}h, h \rangle -2\langle Ah, h \rangle\langle Bh, h \rangle|^2+|\langle [A,B]h, h \rangle |^2}}{2} \end{align*} and \begin{align*} (2) \quad \quad \quad \Delta _h(A)^2+ \Delta _h(B)^2 \geq…
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