Alireza Jamali's Blog
ω≡i∂∂tlogψ
β:=1kBT≡−it
so
βω=t∂∂tlogψ,
thus
eℏωkBT=eℏβω=exp(ℏt˙ψψ).
In operator form
ˆeℏβω=exp(ℏt∂∂t)
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