Preference for the notation used for the wave function?

  • #1
entropy1
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If I am correct, the wave function is presented as a vector in Hilbert Space. Alternatively this vector can be multiplied by the identity operator. Is there a preference for one notation or the other? Are they both possible representations of the same wave function?
 
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  • #2
entropy1 said:
the wave function is presented as a vector in Hilbert Space
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:
this vector can be multiplied by the identity operator
Which leaves it unchanged.

entropy1 said:
Is there a preference for one notation or the other?
They aren't different notations for the state vector.

Where are you getting this from?
 
  • #3
Sorry, I made a mistake.
 
  • #5
PeterDonis said:
How so?
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.
 
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  • Skeptical
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  • #6
entropy1 said:
I was trying, in the finite dimensional Hilbert Space case, to get the amplitudes λi on the diagonal of a matrix.
What does this mean? Again, where are you getting this from? A reference would be very helpful as your own explanations are garbled.
 
  • #7
PeterDonis said:
where are you getting this from?
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.
 
  • #8
entropy1 said:
I don't read scientific articles.

Then where did you get this phrase:
entropy1 said:
in the finite dimensional Hilbert Space case, to get the probability amplitudes <Ψ|ei> on the diagonal of a matrix.

?
 
  • #9
weirdoguy said:
Then where did you get this phrase:
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.
 
  • #10
entropy1 said:
I just have basic questions about physics.
But apparently you can't even frame your questions in a way that anyone else can understand.

entropy1 said:
I was pondering that by myself.
Or even know where you are getting whatever information you are basing your questions on.

This is not a recipe for productive discussion. Thread closed.
 

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