Probability of Electron at x=1.0nm In 0.010nm-Wide Region

[6Stang7]

Ok, so the wave function for an electron that is confined to x>=0nm is:

w(x)=0 for x<0nm
w(X)=be^(-x/6.4nm) for x>=0nm

what is the probability of finding the electron in a 0.010nm-wide region at x=1.0nm?


I have no clue how to even start on this. This is no coverd in my physics book, so I have been trying to find something on the internet, but have come up dry. Anyone have anything that would help to explain this, along with inifinite square wells and realating the ground energy state to the width of the well?

 

[kreil]

probability of finding a particle between x1 and x2:

$$\int_{x_1}^{x_2}P(x)dx=\int_{x_1}^{x_2} | \psi (x) | ^2dx$$

with psi being the wave function.

 

[Dick]

probability of finding a particle between x1 and x2:

$$\int_{x_1}^{x_2}P(x)dx=\int_{x_1}^{x_2} | \psi (x) | ^2dx$$

with psi being the wave function.

Under the assumption that the wavefunction is normalized (integral over all space=1). Yours isn't. Yet.

 

[HallsofIvy]

In other words, first determine b so that
$$b\int_0^\infty e^{-x/6.4}dx= 1$$

Then find
$$b\int_{0.995}^{1.005} e^{-x/6.4}dx$$