- #1
Theodore0101
- 10
- 0
- Homework Statement
- An electron is in state n=2 in an infinite quantum well with width L. What is the probability to find the electron if you measure within the well's central third? Can someone cofirm whether or not my solution is correct
- Relevant Equations
- Y=Asin(n*pi*x/L)
Homework Statement:: An electron is in state n=2 in an infinite quantum well with width L. What is the probability to find the electron if you measure within the well's central third? Can someone cofirm whether or not my solution is correct
Homework Equations:: Y=Asin(n*pi*x/L)
I use the wave funtion Asin(n*pi*x/L) for a wave in a well of the interval 0 to L and square the absolute value of it, getting abs(Asin(n*pi*x/k))^2 = abs(A)^2 *sin^2(n*pi*x/L) (since sin^2(x) is greater or equal to 0) (I use n=2 of course)
I then take the abs(Y)^2 function and integrate it from 0 to L, (using that sin^2(x)`= 1/2(1-cos(2x)) and define the expression as equal to 1 in order to be able to normate it. I get that abs(A)^2*L/2=1 => abs(A)^2 = 2/L
I use 2/L in place of the abs(A)^2 in the integral expression and integrate from L/3 to 2L/3 so that it is the third in the middle. I get that it is equal to 0.229959166. Is this the correct way to solve it? Also, if anyone knows their significant figures, I'm also unsure about how many I am supposed to use in my final answer, since the problem only gives us n=2 which is discrete and that we are calculating for 1/3 of L, and doesn't give any regular values
Thanks
Homework Equations:: Y=Asin(n*pi*x/L)
I use the wave funtion Asin(n*pi*x/L) for a wave in a well of the interval 0 to L and square the absolute value of it, getting abs(Asin(n*pi*x/k))^2 = abs(A)^2 *sin^2(n*pi*x/L) (since sin^2(x) is greater or equal to 0) (I use n=2 of course)
I then take the abs(Y)^2 function and integrate it from 0 to L, (using that sin^2(x)`= 1/2(1-cos(2x)) and define the expression as equal to 1 in order to be able to normate it. I get that abs(A)^2*L/2=1 => abs(A)^2 = 2/L
I use 2/L in place of the abs(A)^2 in the integral expression and integrate from L/3 to 2L/3 so that it is the third in the middle. I get that it is equal to 0.229959166. Is this the correct way to solve it? Also, if anyone knows their significant figures, I'm also unsure about how many I am supposed to use in my final answer, since the problem only gives us n=2 which is discrete and that we are calculating for 1/3 of L, and doesn't give any regular values
Thanks