Concept of Superposition in QM?

[hellomister]

Hi I was just wondering if someone could explain superposition in QM? Is it to get the probability of finding a particle in a certain state of a wavefunction that would have both positive and negative probabilities?

 

[jdwood983]

Hi I was just wondering if someone could explain superposition in QM? Is it to get the probability of finding a particle in a certain state of a wavefunction that would have both positive and negative probabilities?

Whoa! You can never have a negative probability! By definition, probability has a range of 0 to 1! You can never go past either limit!

Superposition is just the idea that if you have two or more functions acting on something, then the net effect is just the sum of the two functions separately:

$$F(x_1+x_2+\cdots)=F(x_1)+F(x_2)+\cdots$$

In QM, if you have two separate wavefunctions that satisfy Schrodinger's equation, say $\psi_1$ and $\psi_2$, then you can create a third wavefunction by adding the two previous together:

$$\psi_3(x)=\alpha\psi_1(x)+\beta\psi_2(x)$$

where I have used $\alpha,\,\beta$ to be just constants that would need to be found in the process of solving the problem(s). The main reason one would want to do this is if $\psi_3$ has a basis that is more applicable to the situation (cases of spin, angular momentum)

Does this help any?