Preference for the notation used for the wave function?

[entropy1]

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?

 

[PeterDonis]

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.

this vector can be multiplied by the identity operator

Which leaves it unchanged.

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?

 

[entropy1]

Sorry, I made a mistake.

 

[PeterDonis]

Sorry, I made a mistake.

How so?

 

[entropy1]

How so?

I was trying, in the finite dimensional Hilbert Space case, to get the probability amplitudes <Ψ|e_i> on the diagonal of a matrix. But in the way I mentioned this is not the case.

 

[PeterDonis]

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.

 

[entropy1]

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.

 

[weirdoguy]

I don't read scientific articles.

Then where did you get this phrase:

in the finite dimensional Hilbert Space case, to get the probability amplitudes <Ψ|ei> on the diagonal of a matrix.

?

 

[entropy1]

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.

 

[PeterDonis]

I just have basic questions about physics.

But apparently you can't even frame your questions in a way that anyone else can understand.

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.