Finding Electron Probability: Wave Function x-Axis Analysis

[UrbanXrisis]

the wave function descrbing a state of an electron confined to move along the xaxis is given at time zero by:

$$\Psi(x,0)=Ae^{\frac{-x^2}{4 \sigma^2}}$$

where sigma is a constant (i believe).

I am asked to find the probability of finding the electron in a degion dx centered at x=0.

I really don't know where to being since the wave function isn't in complex form so I can't multiply it by its complex conjugate. what should I do?

 

[topsquark]

the wave function descrbing a state of an electron confined to move along the xaxis is given at time zero by:

$$\Psi(x,0)=Ae^{\frac{-x^2}{4 \sigma^2}}$$

where sigma is a constant (i believe).

I am asked to find the probability of finding the electron in a degion dx centered at x=0.

I really don't know where to being since the wave function isn't in complex form so I can't multiply it by its complex conjugate. what should I do?

$$P(x)= \Psi ^* \Psi$$ whether the wavefunction is complex or not. So $$P(0) = A^2e^{\frac{-x^2}{2 \sigma^2}}|_{x=0} = A^2$$.

-Dan

PS In case this is the issue, if a is a real number $$a^* = a$$.

 

[UrbanXrisis]

you mean $$P(0,0)$$ right? cause it is with respect to time too, but time is always t=0 in this problem