Trace of Position and Momentum Operator

  • #1
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Homework Statement



Hi guys, I've not started a course on QM yet, but we are currently learning the maths used in QM.


Show, by taking the trace of both sides show that finite dimensional matrix representations
of the momentum operator p and the position operator x which satisfy [p, x] = −ih are not possible.

Why does this argument fail if the matrices are infinite-dimensional (as Heisenberg’s were)?

15plh50.png


Homework Equations





The Attempt at a Solution



Are the position and momentum operators supposed to be matrices? I've looked up on wikipedia, the position operator is more of like ih(d/dp) while the momentum operator is ih(d/dx).
 
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Answers and Replies

  • #2
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I believe this link will help you understand.

http://www.asianscientist.com/books/wp-content/uploads/2013/05/7271_chap02.pdf [Broken]
 
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  • #3
1,734
13
I believe this link will help you understand.

http://www.asianscientist.com/books/wp-content/uploads/2013/05/7271_chap02.pdf [Broken]

It looks difficult but I will give it a go.
 
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