Quantum Mechanics - Superposition of Wavefunctions?

[pearapple]

Homework Statement

The wavefunction for a particle in one dimension is given by
ψ₁. Another state the particle may be in is ψ₂. A third state the particle could be in is ψ₃.

Looking at the wavefunctions, ψ₃ is ψ₁ and ψ₂ added together.

Is the probability of being in a given interval in ψ₃ the same as the separate probabilities for ψ₁ and ψ₂ for that interval?

Homework Equations

The Attempt at a Solution

I don't really understand how superposition works. I read something about the ψ's being linear, so a linear combination of ψ₁ and ψ₂ (ie. ψ₃) is still a solution to the Schrödinger equation.

Is the superposition state a completely different state still though? I don't get why I am being asked this question. If it's a mixture of the two states, the probabilities would change wouldn't they? I don't see the link here.

 

[vela]

Suppose the particle is in the state ψ₁ and say the probability of finding it in the interval a ≤ x ≤ b is p₁. Similarly, suppose the particle is in the state ψ₂ and the corresponding probability is p₂, and likewise for state ψ₃.

The question is asking you, I believe, if it's true that p₃ = p₁ + p₂.

 

[pearapple]

Thanks! I believe you're right.

In general, I don't think p₃ = p₁ + P₂.

I don't think I could explain why though. I just don't see WHY those would be equal, because although state 3 is a superposition, it is still a new state is it not? Is there some situation in which p₃ = p₁ + P₂ is true?