suppose two particle? I'm confused, did you try to describe 2 particles?

@OfekGillon Yes. $|\psi>$ is a suposition of particle $|A>$ and $|B>$ normalized by $c_1,c_2$. Particle $|A>$ is normalized with respect to state vector $|u_1>,|u_2>$ by $a_1,a_2$. Particle $|B>$ is normalized with respect to state vector $|u_1>,|u_2>$ by $b_1,b_2$.

Why do you normalize two particles? Why do you add them? When having two particles you should use a tensor product

@OfekGillon It's $|c_1|^2$ portion/probability of particle $A$ and $|c_2|^2$ for particle $B$. The measurement $|A><A|+|B><B|$ obtain either particle $A$ or $B$, yet, if one add them together, the secondary result for measurement $|u_1><u_1|+|u_2><u_2|$ is differed. (Acturally, if you add them together, the sate is no longer normalized)

What does it mean to have a $|c_1|^2$ probability of a particle? Can you please give an example?

@OfekGillon Suppose a mixure of $N$ particles with $|c_1|^2 N$ of particle $A$. Or shot single particles with probability of obtian $A$ to be $|c_1|^2$.

Ok, then that's not a wave function comprised of a quantum superposition

@OfekGillon what do you mean? $|\psi>=c_1 A+c_2 B$, en.wikipedia.org/wiki/Quantum_superposition#Theory It's either indistinguishable quantum particles of $A$ or $B$ or a single particle of superposition $A$ and $B$.

The examples in wikipedia aren't two different particles - it is the same particle with probabilities being in two different states.

@OfekGillon so the measurement of $|u_1>$ and $|u_2>$ collapse the states into $|A>$ and $|B>$ before the measurement? How could that be? I didn't measure perform the measurement $|A><A|+|B><B|$..

Well hellos

hello*

?

hello?

I think your having a little confusion with the notations in quantum mechanics

are you new to the topic?

Not really, but I'm new to state vector formalism

Really? That's usually how most start in QM. Which other formalism are you familiar with?

wave vector, or matrix

what's the difference between wave vector and state vector?

can you please give an example of usage with the other 2?

Sir?

I'm not sure how to say this

but bascially states vector use hilbert space, wave funciton use functional expension, and matrix use matrix.

the hilbert space formalism is just the general case of the wave function idea

Say you have a particle in a box

the eigen states of the hamiltonian look like $\sin (\frac{\pi n}{L} x ) $

sin(pi n/L x)

right?

not really, there is a siginificant difference between wave and states. Think about spin, there is no function for it. On the other hand, what's the states for a hydrogon atom's sphere?

states is more abstruct, wave is limited.

ofcourse, I said it is a generalization

but for the hydrogen atom you can write states

No, hydrogen atom's electron orbit always use funciton, you are consusing two concepts.

you can write them in state formalism... functions are just one way to represent some states

You can't "draw some spherical graph of the continuous orbit" with state vector formalism.

are you answering the question?

But you can represent the same idea. Why right the explicit form of the orbital if you can just write it as |n l m>

get what I'm saying?

No, you are not getting what's the difference between them, like I said, what happend to spin?

Funcitonal represtation is somewhat "determinsistic".

In functional represtation, if you can write spin in a funciton, then its probabilistic evoluation is determined, that's bascially wrong.

you mean time evolution of the wave function is deterministic, but not of a state vector?

In sate vector formalism, the modern approach usually assume hilber space to be finite, which means it can not describe continuous orbit.

"the modern approach usually assume hilber space to be finite" - actually that's not correct

Where did you read that?

Can you give a source?

If you are beliving in and are going to write infinite bars and kets on a paper, fine, you can say that it seemed to be infinite to you, but even if you spend all your time wiritng a single states, you won't finish it and the symbol you wrote was sitll finite.

What? are you trying you don't "believe" in infinite dimension vector spaces?

You can say the same thing about fourier series

and the fourier transform

State vectors are the more general, abstract way to represent your quantum state. We get wave functions when we represent these abstract state vectors in certain bases.

In other words, wave functions depend on the basis. State vectors do not