# Wave function

A particle moving on a straight line is described by $$\psi(x)=\frac{1+ix}{1+ix^2}$$.
Where is the particle likely to be found?
I took the derivative of probability density with respect to x and equated it to 0. I got my answer to be x=0.643,-0.643,1.554i and -1.554i.
Please tell me whether I am right or wrong or are there any other methods to solve this problem or not?

## Answers and Replies

dx
Homework Helper
Gold Member
There is no reason for the expectation value to be at a stationary point of the probability density.

You have to evaluate the integral <x> = ∫ψ*(x)xψ(x)dx = ∫xP(x)dx.

But the question is about maximum probability of finding the particle, isn't it?

dx
Homework Helper
Gold Member
"Where is the particle likely to be found" usually means that they want you to find the expectation value of x.

dx
Homework Helper
Gold Member
Unless the exact wording of the question was "where is the particle most likely to be found". Then you would find the x which maximises P(x).

So if the question is where the particle is most likely to be found, is my answer correct.

dx
Homework Helper
Gold Member
x is a real number, how did you get imaginary values?

By factorising

Now I finally got it, thanks dx