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 wave function notation is a mathematical representation used to describe the quantum state of a physical system. It is denoted by the Greek letter psi (ψ) and is a function of the position and time of the system.
The wave function notation is important because it allows us to understand and predict the behavior of quantum systems. It is a fundamental concept in quantum mechanics and is used in many areas of physics, chemistry, and engineering.
The Dirac notation, also known as bra-ket notation, uses the symbols ⟨ and ⟩ to represent the quantum state and its corresponding dual state, respectively. The Schrödinger notation uses the wave function symbol ψ and its complex conjugate ψ* to represent the quantum state and its dual state. Both notations are equivalent and can be used interchangeably.
The wave function notation is related to probability through the Born rule, which states that the probability of finding a particle at a certain position is equal to the magnitude squared of the wave function at that position. In other words, the wave function represents the probability amplitude of finding a particle at a specific location.
Yes, the wave function notation can be used for all types of physical systems, as long as they follow the laws of quantum mechanics. This includes particles, atoms, molecules, and even larger systems like crystals and superconductors.