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Question about microstates and electrons

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Problem Statement
Attached
Relevant Equations
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In 8a) I don't understand the question, does spin = 1/2 mean the magnitude of the spin or the z-component of the spin is 1/2? Can the electrons possess be any of the spin=1/2 or -1/2? Are the electrons distinguishable?
 

DrClaude

Mentor
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3,007
Spin-1/2 refers to the spin quantum number, so the electrons are free to have their spin point along any direction. On that subject, part (d) is not well formulated: it should specify ##s_z##, not just ##s##.

The electrons are indistinguishable, as stated in the problem. (Generally speaking, quantum particles should always be considered indistinguishable unless specified otherwise or due to a particular physical situation, like atoms in a crystal.)
 

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