I What does a superposition of states mean in quantum mechanics?

[Karolus]

ok , "mixed" states ( density matrix etc) are different from superposition state, not overcomplicate with english..

 

[Karolus]

The analogy is actually pretty direct. If the unit direction vector along a horizontal line is $|H\rangle$, and the unit direction vector along a vertical line is $|V\rangle$, then the unit direction vector for the diagonal line X=Y is $\frac{1}{\sqrt 2} |H\rangle + \frac{1}{\sqrt 2} |V\rangle$. Look familiar?

When you say that $\frac{1}{\sqrt 2} |0\rangle + \frac{1}{\sqrt 2} |1\rangle$ is simultaneously both 0 and 1, it's exactly like saying that the line along $\frac{1}{\sqrt 2} |H\rangle + \frac{1}{\sqrt 2} |V\rangle$ is simultaneously along H and V. It's a type error. You can decompose a diagonal line's direction into the HV basis, but that doesn't mean the diagonal line is secretly made up of horizontal and vertical line segments.

Here there is some error, some approximation and some terminological confusion ... "simultaneously"! To say that a diagonal is the superposition of horizontal and vertical, mmm ... seems Hegel ... But if we speak of a vector, and its decomposition into two "basic" vectors, horizontal and vertical, or if you prefer, i and j with factors appropriate, then we are talking about linear algebra, and we found the hot water ... so, the principle of superposition has a clear formulation as a linear combination of vectors: a vector (state) can be expressed as a superposition (linear combination) of other states (vectors). That's all? It seems to you, according to your conception of the "superposition principle" is nothing more than an elementary math simple rules ... so it seems ...
I think indeed that the general superposition principle of quantum mechanics applies to the states of any dynamic system. It consists in the hypothesis that relations between these states exist characteristics such that, whenever said system is in a defined state, it can be considered as belonging simultaneously to two or more others.

 

[mike1000]

I deleted this post and I used it to create a new thread. Here is a link to that thread.

https://www.physicsforums.com/threads/more-on-superposition.909502/