Timeline for Contradictory statements on product states for distinguishable particles in Quantum Mechanics

9 events

when toggle format	what		by	license	comment
Jan 22, 2021 at 18:01	comment	added	Steven Sagona		Oh I see, they are three separate examples.
Jan 22, 2021 at 17:58	comment	added	J. Murray		@StevenSagona There's not really any math to be done, I meant to give an example of an element of $V\otimes W$ which cannot be written as $v\otimes w$ for some $v\in V$ and $w\in W$. Such elements do not exist in the direct sum space $V\oplus W$.
Jan 22, 2021 at 17:41	comment	added	Steven Sagona		I can't follow the math done in the tensor product example. Is there a typo on this line that says "cannot be combined or simplified!" ?
Jan 22, 2021 at 16:40	history	edited	BioPhysicist	CC BY-SA 4.0	edited body
Jan 22, 2021 at 12:17	comment	added	J. Murray		@ApoorvPotnis I updated my answer to address your question.
Jan 22, 2021 at 12:17	history	edited	J. Murray	CC BY-SA 4.0	added 1753 characters in body
Jan 22, 2021 at 11:08	comment	added	Apoorv Potnis		My professor's notes say that for the direct sum, $V$ and $W$ should not have any common vector except the zero vector. $\operatorname{dim}{(V \oplus W)} = \operatorname{dim}{(V)} + \operatorname{dim}{(W)}$.
Jan 22, 2021 at 1:06	history	edited	J. Murray	CC BY-SA 4.0	added 85 characters in body
Jan 21, 2021 at 15:54	history	answered	J. Murray	CC BY-SA 4.0