Is Psi = Superposition?

[QuantumT]

Is psi (Ψ) identical to "superposition"?

Or are they two different properties?

The reason I ask, is because I've never been able to find a straight answer.

[Mordred]

It's commonly used to define a state. The state can be determined or in superposition.

[QuantumT]

Just now, Mordred said:

It's commonly used to define a state. The state can be determined or in superposition.

So the wave function and the superposition are identical?

[Strange]

Just now, QuantumT said:

So the wave function and the superposition are identical?

The wave function describes the state; and in the case of superposition it describes the superposition of states.

[QuantumT]

7 minutes ago, Strange said:

The wave function describes the state; and in the case of superposition it describes the superposition of states.

So the wave function is ambiguous, and the superposition is dual?

What I'm trying to settle is if "wave function" and "superposition" are two expressions of the same phenomenon?

Edited August 3, 2019 by QuantumT

[Mordred]

Every state or super position of states are described by wave function. The two won't have the same wave function but both states are described by them

[QuantumT]

2 minutes ago, Mordred said:

Every state or super position of states are described by wave function. The two won't have the same wave function but both states are described by them

Thanks! So what other states does the WF include, besides SP?

[Strange]

21 minutes ago, QuantumT said:

So the wave function is ambiguous, and the superposition is dual?

What I'm trying to settle is if "wave function" and "superposition" are two expressions of the same phenomenon?

A single particle that is not in a superposition of state will still be described by a wave function. 

Two particles that are entangled will be described by a single wave function (which is what entanglement means).

 

[QuantumT]

Thanks for your patience guys.

Just to eliminate misunderstandings:
So you can detect a particle, and collapse its wave function, without measuring its spin? And thereby keep it in a superposition?

[swansont]

2 hours ago, QuantumT said:

Thanks for your patience guys.

Just to eliminate misunderstandings:
So you can detect a particle, and collapse its wave function, without measuring its spin? And thereby keep it in a superposition?

As long as the spin isn’t the state in superposition

3 hours ago, QuantumT said:

So the wave function is ambiguous, and the superposition is dual?

What I'm trying to settle is if "wave function" and "superposition" are two expressions of the same phenomenon?

A superposition is described by a wave function, but requires that the particle be in two states. If it’s in a single state, it’s still described by a wave function.

[Amazing Random]

We dont know what the wave function physically represents  . But we dont actually need to use QM to application . Just the Ψ^2 expresses the propability of finding a subatomic particle at a certain position.

[timo]

This post is a bit beyond the original question, which has been answered - as Psi being a common Greek letter to label a wave function and wave functions being used to describe (all) quantum mechanical states. I do, however, have the feeling that I do not agree with some of what your replies seem to implicate about superposition, namely that it is a special property of a state. So I felt the urge to add my view on superposition.

 

Fundamentally, superposition is not a property of a quantum mechanical state. It is a property of how we look at the state - at best. Consider a system in which the space S of possible states is spanned by the basis vectors |1> and |2>. We tend to say that [math] |  \psi  _1 > = (|1> + |2>)/ \sqrt{2} [/math] is in a superposition state and [math] |  \psi _2 > = |1>[/math] is not. However, [math] |A> = (|1> + |2>) / \sqrt{2} [/math] and [math] |B> = (|1> - |2>) / \sqrt{2} [/math] is just as valid as a basis vectors for S as |1>  and |2> are. In this base, [math] |  \psi  _2 > = (|A> + |B>)/ \sqrt{2} [/math] is the superposition state and [math] |  \psi _1 > = |A>[/math] is not. There may be good reasons to prefer one base over the other, depending on the situation. But even in these cases I do not think that superposition should be looked at a property of the state, but at best as stemming from the way I have chosen to look at the state.

 

Personally, I think I would not even use the term superposition in the context of particular states (a although a search on my older posts may prove that wrong :P). I tend to think of it more as the superposition principle, i.e. the concept that linear combinations of solutions to differential equations are also solutions. This is kind of trivial, and well known from e.g. the electric field. The weird parts in quantum mechanics are 1) the need for the linear combination to be normalized (at least I never could make sense of this) and 2) that states that seem to be co-linear by intuition are perpendicular in QM. For example, a state with a momentum of 2 Ns is not two times the state of 1 Ns but an entirely different basis vector. Superposition in this understanding almost loses any particularity to QM.

 

Edit: Wrote 'mixed' instead of 'superposition' twice, which is an entirely different concept. Hope I got rid of the typos now.

Edited August 6, 2019 by timo