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.
The most common notations used for the wave function are Ψ (Psi) and φ (phi). These symbols are widely accepted in quantum mechanics to represent the wave function, which describes the quantum state of a system.
Ψ (Psi) is often preferred because it has been historically used since the early days of quantum mechanics, making it a well-recognized symbol among physicists. Its widespread use in textbooks and research papers also contributes to its preference.
Yes, φ (phi) is sometimes used in specific contexts, such as when dealing with spherical harmonics or angular components of wave functions. It can also be used to distinguish between different types of wave functions within the same problem.
No, the choice of notation does not affect the interpretation of the wave function. The notation is simply a symbol used to represent the mathematical function, and the physical interpretation remains the same regardless of the symbol used.
While Ψ (Psi) is the most commonly used notation, there is no strict standard, and different authors may use different symbols based on their preference or the specific context of their work. However, Ψ (Psi) remains the most universally recognized and accepted notation.