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Qmechanic ♦
Qmechanic ♦
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In http://en.wikipedia.org/wiki/Measurement_in_quantum_mechanics#Degenerate_spectra, it is said that

If there are multiple eigenstates with the same eigenvalue (called degeneracies),..., The probability of measuring a particular eigenvalue is the squared component of the state vector in the corresponding eigenspace, and the new state after measurement is the projection of the original state vector into the appropriate eigenspace.If there are multiple eigenstates with the same eigenvalue (called degeneracies),..., The probability of measuring a particular eigenvalue is the squared component of the state vector in the corresponding eigenspace, and the new state after measurement is the projection of the original state vector into the appropriate eigenspace.

My question: Is the state vector after measurement when the eigenspace is degenerated a pure state or mixed state? And what is the mathematical formulation of the mentioned "projection" onto the eigenspace?

In http://en.wikipedia.org/wiki/Measurement_in_quantum_mechanics#Degenerate_spectra, it is said that

If there are multiple eigenstates with the same eigenvalue (called degeneracies),..., The probability of measuring a particular eigenvalue is the squared component of the state vector in the corresponding eigenspace, and the new state after measurement is the projection of the original state vector into the appropriate eigenspace.

My question: Is the state vector after measurement when the eigenspace is degenerated a pure state or mixed state? And what is the mathematical formulation of the mentioned "projection" onto the eigenspace?

In http://en.wikipedia.org/wiki/Measurement_in_quantum_mechanics#Degenerate_spectra, it is said that

If there are multiple eigenstates with the same eigenvalue (called degeneracies),..., The probability of measuring a particular eigenvalue is the squared component of the state vector in the corresponding eigenspace, and the new state after measurement is the projection of the original state vector into the appropriate eigenspace.

My question: Is the state vector after measurement when the eigenspace is degenerated a pure state or mixed state? And what is the mathematical formulation of the mentioned "projection" onto the eigenspace?

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Siyuan Ren
Siyuan Ren
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How does a state vector be projected onto an eigenspace after measurement

In http://en.wikipedia.org/wiki/Measurement_in_quantum_mechanics#Degenerate_spectra, it is said that

If there are multiple eigenstates with the same eigenvalue (called degeneracies),..., The probability of measuring a particular eigenvalue is the squared component of the state vector in the corresponding eigenspace, and the new state after measurement is the projection of the original state vector into the appropriate eigenspace.

My question: Is the state vector after measurement when the eigenspace is degenerated a pure state or mixed state? And what is the mathematical formulation of the mentioned "projection" onto the eigenspace?