The quantum mechanical Hilbert space is defined as a complex vector space that is complete and has an inner product defined on it. Please help me understand the meaning of "complete" in this definition, and also the reason why this property is needed. Thanks.
Asked
Active
Viewed 41 times
1
-
This was already discussed https://mathoverflow.net/q/35840/ – Ralf Ulrich Aug 24 '21 at 19:00
-
1It is complete in the sense of Cauchy sequence. Many mathematical constructions actually depend on this completeness property. You can refer to this lecture notes on Quantum mechanics by Schuller : http://mathswithphysics.blogspot.com/ – KP99 Aug 24 '21 at 19:51
-
@KP99 Thanks, I'll look into it. – Solidification Aug 25 '21 at 01:14