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Results tagged with complex-numbers
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user 186989
Numbers of the form $\{z= x+ i\,y:\;x,\, y\in\mathbb{R}\}$ where $i^2 = -1$. Useful especially as quantum mechanics, where system states take complex vector values.
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Why do we say $\exp(-iHt)$ is holomorphic for $t$ in the lower half plane when $H>0$?
I've seen this statement in many papers. However the function $e^{-iHt}$ satisfies the Cauchy-Riemann condition for all t. So why do we say $e^{-iHt}$ is holomorphic in the lower half plane specifical …
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