OKWaveCommunity

"complete" Hilbert space ?


Let's Sign Up now! (For free)
FAQ(FAQ) Any troubles?
Categories
[ More ]
TOP
Education
Q&A Menu
Recent Questions
Recent Answers
Recent Thank You's
Popular Q&A's
Helpful Q&A's

[ Advanced ]
Ask  

400 characters left.    Click here if you need more characters to work with..


Question
QNo.20000582 "complete" Hilbert space ?
ID:py_seminar Question From ”JJ Sakurai Modern Quantum Mechanichs seminar”
* I'm Japanese. Sorry for my poor English.
* I'll appreciate if you correct my mistake in English.

I don't know what "complete" in Hilbert space means.

Could you tell me in more plain words?

I got the answer from someone :

there is two types of meaning

1. Complete in metric space
It is defined by the convergence of arbitrary Cauchy sequence.

2. Complete in orthogonal system
Every vector in this space can be written as a linear combination of base vectors.

And there is no relation between these two.


Is this correct?

And if this is correct, Which one is the correct definition of "complete" in Hilbert space (in JJ Sakurai's book).
Priority Level:
  • Immediately an answer!
Date Posted:
09/07/15 11:19
 
To the top of this page