# Wave Function Probability

1. Nov 6, 2008

I was reading part of a book which was explaining about the probability of finding a partical on a 1d line.
$$\int^{+\infty}_{-\infty}$$P(x) dx = 1
This sounds right because if the line was infinitely long then the partical must be on it.
You can them intergrate between a and b to find the probability of it being in a lenght and if a and b were the same the probability would be 0.
But when you intergrate P(x) dx you get $$\frac{Px^{2}}{2}$$
by putting the numbers in you get P$$\infty$$ - -P$$\infty$$
or P$$\infty$$ + P$$\infty$$ = P$$\infty$$
A probability can't be more than 1. I must be missing something or dealing with the infinities in the wrong way.
(Sorry it looks like P^infinity its P x infinity but I couldn't change it.)

2. Nov 6, 2008

### cks

$$\int_\infty^\infty P(x) dx=1$$ doesn't mean $$\int_\infty^\infty Px dx=1$$ P(x) means the probability in function of x not P a constant times x.

3. Nov 6, 2008

### f95toli

?

If you integrate P(x) dx you get the integral of P(x); I am not quite sure why you think you would get $$\frac{Px^{2}}{2}$$?
P(x) is a FUNCTION, not a constant; there is no way to integrate it unless you know what that function is.

4. Nov 6, 2008

Oh so P(x) is the wave function? I'm going to read the chapter again.

5. Nov 6, 2008

### Manilzin

No, P(x) is the probability function, which is the wavefunction squared (actually, absolute value squared)... So P(x)dx gives the probability for finding the particle on a bit of length dx at position x.

6. Nov 6, 2008