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Ensembles for spin one half
Ensembles for spin one half
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Mixed ensemble averages
In [1], Sakurai leaves it to the reader to verify that knowledge of the three ensemble averages [S_x], [S_y],[S_z] is sufficient to reconstruct the density operator for a spin one half system.
I’ll do this in two parts, the first using a spin-up/down ensemble to see what form this has, then the general case. The…
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PHY1520H Graduate Quantum Mechanics. Lecture 3: Density matrix (cont.). Taught by Prof. Arun Paramekanti
PHY1520H Graduate Quantum Mechanics. Lecture 3: Density matrix (cont.). Taught by Prof. Arun Paramekanti
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Disclaimer
Peeter’s lecture notes from class. These may be incoherent and rough.
These are notes for the UofT course PHY1520, Graduate Quantum Mechanics, taught by Prof. Paramekanti, covering [1] chap. 3 content.
Density matrix (cont.)
An example of a partitioned system with four total states (two spin 1/2 particles) is sketched in fig. 1.
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PHY1520H Graduate Quantum Mechanics. Lecture 2: Basic concepts, time evolution, and density operators. Taught by Prof. Arun Paramekanti
PHY1520H Graduate Quantum Mechanics. Lecture 2: Basic concepts, time evolution, and density operators. Taught by Prof. Arun Paramekanti
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Disclaimer
Peeter’s lecture notes from class. These may be incoherent and rough.
These are notes for the UofT course PHY1520, Graduate Quantum Mechanics, taught by Prof. Paramekanti, covering chap 1 (basic concepts),3 (density operator). content from [1].
Basic concepts
We’ve reviewed the basic concepts that we will encounter in Quantum…
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Entropy when density operator has zero eigenvalues
Entropy when density operator has zero eigenvalues
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In the class notes and the text [1] the Von Neumann entropy is defined as
\begin{equation}\label{eqn:densityMatrixEntropy:20} S = -\textrm{Tr} \rho \ln \rho. \end{equation}
In one of our problems I had trouble evaluating this, having calculated a density operator matrix representation
\begin{equation}\label{eqn:densityMatrixEntropy:40} \rh…
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