# Questions tagged [trace]

Use this tag when having questions concerning expressions with the trace of a matrix/operator.

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### Problem understanding expectation value of operators defined with density operator in quantum mechanics

I have a problem in understanding why we can write the expectation value of an operator $\hat{O}$ as the trace of $\hat{\rho}\hat{O}$ where $\hat{\rho}$ is the density matrix defined for pure state. ...
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### Order in taking density matrix trace

I remember that for infinite dimensional Hilbert space, the trace is not cyclic, for example, for harmonic oscillators, then we have $$Tr(aa^{\dagger})\neq Tr(a^{\dagger}a)$$ Then, when we calculate ...
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### Metric tensor times its inverse using Kronecker delta

From tensor calculus, we know that $$g^{\mu\nu}=\delta_{\lambda}^{\mu}\delta_{\phi}^{\nu}g^{\lambda\phi}.\tag{1}$$ Based on (1), is the following true? g^{\...
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### What is the physics meaning of the "trace" (Tr) and how we can calculate it? [duplicate]

What is the physics meaning of the "trace" (Tr) and how we can calculate it? $$Z=tr\left \{ e^{\left ( -H \right )} \right \}$$ Where Z is the partition function .
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