The wave function in quantum mechanics is represented as a vector in Hilbert Space, and this vector can be multiplied by the identity operator without changing its value. There is no preference for one notation over the other, as both represent the same quantum state. The discussion highlights confusion regarding the relationship between probability amplitudes and eigenvalues in finite-dimensional Hilbert Spaces, emphasizing the need for clarity in framing questions about quantum mechanics.
PREREQUISITESStudents of quantum mechanics, physicists seeking clarification on wave function notation, and anyone interested in the mathematical foundations of quantum theory.
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.