What Happens When a Collapsed and Non-Collapsed Wave Function Combine?

[Einstein's Cat]

For theoretical sake, would a collapsed wave function combined with a non-collapsed wave function result in a wave function between that of a collapsed and non- collapsed wave function? Thank you and please excuse the stupidity of the question

 

[Nugatory]

For theoretical sake, would a collapsed wave function combined with a non-collapsed wave function result in a wave function between that of a collapsed and non- collapsed wave function? Thank you and please excuse the stupidity of the question

You are misunderstanding how collapse works. A wave function that is collapsed in one basis is uncollapsed in another, so it doesn't make a lot of sense to talk about about "adding" a collapsed and an uncollapsed wave function.

You're going to have to work through the question in your other thread (https://www.physicsforums.com/threads/wave-function-equation.830480/), which is going to require some quality time with an introductory QM textbook, to understand why the question in this thread is ill-posed.

 

[Strilanc]

For theoretical sake, would a collapsed wave function combined with a non-collapsed wave function result in a wave function between that of a collapsed and non- collapsed wave function? Thank you and please excuse the stupidity of the question

If you take a qubit that has been measured as being in the state $\left| 0 \right\rangle$ and put it next to a qubit in the superposition $\alpha \left| 0 \right\rangle + \beta \left| 1 \right\rangle$, you have a system of two qubits and the state of the system is $\alpha \left| 00 \right\rangle + \beta \left| 01 \right\rangle$. That's one way to "combine" a collapsed state with a non-collapsed state and get a meaningful larger state out.

An individual qubit can't be in a superposition of both collapsed and not collapsed. It can be in a mixed state, but a mixed state is a probability distribution of superpositions. Having a superposition of probability distributions instead of a probability distribution of superpositions is putting things the wrong way around math-wise.