# Electron wave function and Probability

1. May 21, 2012

### bayan

1. The problem statement, all variables and given/known data

I've been asked to find the value of c and the probability that the electron is located in the range of x=-1 and x=1.

2. Relevant equations

See Graph below

3. The attempt at a solution

ψ graph http://img850.imageshack.us/img850/61/wavefunction.jpg [Broken]

|ψ|$^{2}$ graph http://img35.imageshack.us/img35/6663/psisquare.png [Broken]
As mentioned by ehild the graph is not drawn with correct scale (my carelessness, which caused all my problems)

For part a) I need to find value of C. Which I have found to be 0.577 but the answer seems wrong, I have done this by drawing a |ψ|$^{2}$ graph (which is almost the same except there are no negative y values. I have found c by making the area underneath |ψ|$^{2}$ equal to 1. Since the two smaller square in -1to -2 and 1 to 2 are exactly half I tried to find c by making the graph a rectangle with L=3nm given area must equal 1, width must equal $\frac{1}{3}$. Hence I got a value for c which is $\sqrt{\frac{1}{3}}$ = 0.577

For part b I am asked to fin probability of electron being in x=-1 and x=1 nm. My answer was 0.666 (0.7 as I have been asked to answer in one significant figure) but this seems wrong too.

Anyone able to tell me where I have made mistake?

Thanks

Last edited by a moderator: May 6, 2017
2. May 21, 2012

### ehild

.... and the height of the middle part is 4 times the height of the small rectangles. So you have got two rectangles of width 1 and height c2/4 and a big rectangle of width 2 and height c2.
What is the area?

ehild

3. May 21, 2012

### bayan

Thanks.

Edit: Obviously I need to work a bit more on wave functions and finding the heights, anyone know where I could get some examples? I tried google, but it comes up with complex stuff.

Last edited: May 21, 2012