Phy5645/Double pinhole experiment: Difference between revisions
(New page: Submitted by team 1 ------ '''Question: Double Pinhole Experiment''' Besides Stern-Gerlach experiment, double slit experiment is another one that demonstrates how different quantum mech...) |
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[[Image:Double_pinhole_1.JPG]] | [[Image:Double_pinhole_1.JPG]] | ||
Suppose you send in an electron along the z axis on a screen at <math>z = 0</math> with two pinholes at <math>x = 0, y = \pm d/2</math>. On a point <math>(x,y)</math> on another screen at <math>z = L>>d, \lambda,</math> the distance from each pinhole is given by <math> r_{\pm}=\sqrt{x^{2}+(y\mp d/2)^{2}+L^{2}}</math>. | Suppose you send in an electron along the z axis on a screen at <math>z = 0</math> with two pinholes at <math>x = 0, y = \pm d/2</math>. On a point <math>(x,y)</math> on another screen at <math>z = L>>d, \lambda,</math> the distance from each pinhole is given by <math> r_{\pm}=\sqrt{x^{2}+(y\mp d/2)^{2}+L^{2}}</math>. The spherical wave from each pinhole is added on the screen and hence the wavefunction is | ||
:<math>\psi(x,y)=\frac{e^{ikr_{+}}}{r_{+}}+\frac{e^{ikr_{-}}}{r_{-}}</math>, | |||
where <math> k = 2\pi /\lambda\!</math>. Answer the following questions. | |||
(a) Considering just the exponential factors, show that the constructive interference appears approximately at | |||
:<math> \frac{y}{r}=n\frac{\lambda}{d}</math> | |||
where <math> r=\sqrt{x^{2}+y^{2}+L^{2}}</math>. | |||
(b) Make a plot of the intensity <math>|\psi(0,y)|^{2}\!</math> as a function of <math>y\!</math>, by choosing <math>k=1, d =20\!</math>, and <math> L=1000 \!</math> | |||
Revision as of 21:58, 5 December 2009
Submitted by team 1
Question: Double Pinhole Experiment
Besides Stern-Gerlach experiment, double slit experiment is another one that demonstrates how different quantum mechanics is from the classic counterpart. To avoid mathematical complications with Bessel function, we discuss two pinholes rather than slits.
Suppose you send in an electron along the z axis on a screen at with two pinholes at . On a point on another screen at the distance from each pinhole is given by . The spherical wave from each pinhole is added on the screen and hence the wavefunction is
- ,
where . Answer the following questions.
(a) Considering just the exponential factors, show that the constructive interference appears approximately at
where .
(b) Make a plot of the intensity as a function of , by choosing , and
