The discussion centers on the notation used for the wave function in quantum mechanics, specifically whether it is preferable to represent the wave function as a vector in Hilbert Space or as a vector multiplied by the identity operator. Participants explore the implications of these representations and their equivalence.
Participants do not reach a consensus on the preference for notation or the clarity of the concepts discussed. Multiple competing views and uncertainties remain throughout the conversation.
Some participants express a lack of familiarity with scientific literature and foundational concepts in quantum mechanics, which may affect the clarity and depth of the discussion.
More precisely, the quantum state is a vector in a Hilbert Space. The wave function is a particular representation of vectors in particular Hilbert Spaces.entropy1 said:the wave function is presented as a vector in Hilbert Space
Which leaves it unchanged.entropy1 said:this vector can be multiplied by the identity operator
They aren't different notations for the state vector.entropy1 said:Is there a preference for one notation or the other?
How so?entropy1 said:Sorry, I made a mistake.
I was trying, in the finite dimensional Hilbert Space case, to get the probability amplitudes <Ψ|ei> on the diagonal of a matrix. But in the way I mentioned this is not the case.PeterDonis said:How so?
What does this mean? Again, where are you getting this from? A reference would be very helpful as your own explanations are garbled.entropy1 said:I was trying, in the finite dimensional Hilbert Space case, to get the amplitudes λi on the diagonal of a matrix.
I don't read scientific articles. I am not a scientist. I understand if you want to keep the forum tidy. I just have basic questions about physics.PeterDonis said:where are you getting this from?
entropy1 said:I don't read scientific articles.
entropy1 said:in the finite dimensional Hilbert Space case, to get the probability amplitudes <Ψ|ei> on the diagonal of a matrix.
I was pondering that by myself. My only knowledge of QM comes from "QM the absolute minimum" by Susskind & co, and PF. I confused the eigenvalue with the probability amplitude. There is a lot I don't understand.weirdoguy said:Then where did you get this phrase:
But apparently you can't even frame your questions in a way that anyone else can understand.entropy1 said:I just have basic questions about physics.
Or even know where you are getting whatever information you are basing your questions on.entropy1 said:I was pondering that by myself.