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Particle in a Box

  • Thread starter ahhppull
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  • #1
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Homework Statement



What is the probability, P, of locating a particle between x = 0 (the left-hand end of
a box) and x = 0.2 nm in its lowest energy state in a box of length 1.0 nm?

Homework Equations



Probability = ∫ψ2dx
ψ = (2/L)1/2sin(n∏x)

The Attempt at a Solution



ψ2 = (2/L)sin2(n∏x)
∫(2/L)sin2(n∏x)dx = 2/L [x/2 - (L/n∏x)sin(2n∏x/L)] from x = 0 to x = 0.2

I plugged in the numbers n=1 and L = 1 and got about 0.2.
The answer is 0.05.
 

Answers and Replies

  • #2
TSny
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ψ2 = (2/L)sin2(n∏x)
∫(2/L)sin2(n∏x)dx = 2/L [x/2 - (L/n∏x)sin(2n∏x/L)] from x = 0 to x = 0.2
Check the factor highlighted above. Note that this factor should have the dimensions of length.
 
  • #3
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Isn't this advanced physics?
 
  • #4
TSny
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Isn't this advanced physics?
Not necessarily. The particle in a box is often covered in the introductory calculus-based physics course (usually in the 3rd semester of the course in the U.S.).
 
  • #5
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Check the factor highlighted above. Note that this factor should have the dimensions of length.
I still don't understand.

I may have wrote something wrong.
The part that you highlighted should be: (L/n∏)
 
  • #6
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I got the answer now, but by changing my calculator to radians when calculating sin(2n∏x/L). Am I suppose to use radian instead of degrees?
 
  • #7
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Yes you are... you are working with numbers here, not with angles... in this case the sine is just a function, and want an adimensional argument. While radians are a conventional unit for angles but are not a real units (you call radians to understand that you are speaking of angles but it is still a pure number), degrees are indeed an unit, so you can't use them here
 
  • #8
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Yes, well done, you're right, radians always for this sort of thing. Took me ages to get used to that.
 
  • #9
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Yes you are... you are working with numbers here, not with angles... in this case the sine is just a function, and want an adimensional argument. While radians are a conventional unit for angles but are not a real units (you call radians to understand that you are speaking of angles but it is still a pure number), degrees are indeed an unit, so you can't use them here
Ok...Thanks!
 

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