Completeness of basis in quantum mechanics

  • #1
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In a QM course,
I learn that an operator can be represented by basis vectors
If the basis vector is complete, the following relation holds
There exist coefficient Mij such that
Sigma Mij |i > < j|. = I , |i> is the basis! and I is the identity matrix

But isn't that in linear algebra
We call the set of basis is complete when
Any vector can be expressed into their linear combination

I wonder why here we seems have 2 definition of completeness
 

Answers and Replies

  • #2
1,734
13
I recommend reading of Sakurai's Book on QM - read the introductory chapters.
 
  • #3
BvU
Science Advisor
Homework Helper
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I wonder why here we seems have 2 definition of completeness
There is only one definition if the two renderings are equivalent, right ? And they are equivalent!
 

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