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The screen is the Y axis and the line perpendicular to it is the X axis. We fire an electron with a well-defined momentum $p_x$ in the X direction. Shouldn't the x-co-ordinate of the particle follow a probabilistic distribution of wavelength $\frac{p_x}{h}$? Then how come we observe a probabilistic distribution along the Y axis instead (the screen)?

Qmechanic
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Egg Man
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    Does this answer your question? Does an electron gain Energy passing through a small slit? – Roger V. Sep 27 '21 at 13:51
  • @RogerVadim Kind of. I still dont completely get it. So the slits make the electron's position a superposition of the two slit locations. This causes an uncertainty in momentum along the Y axis. Because of the initial uncertain momentum, the electrons are detected at probabilistic locations at a later time when they meet the screen. Is this it? – Egg Man Sep 28 '21 at 02:05
  • @RogerVadim So if encountering the slits changes the wave function of the electron, is it then irrelevant that we initially fired an electron in a momentum eigenstate? How come the interference pattern has a wavelength $\frac{p}{h}$, where $p$ is the moment we fired it with? – Egg Man Sep 28 '21 at 02:07
  • I think the difficulty here is due to mixing firing if electron at a certain moment/point, with the wave function, which is the solution of the Schrödinger equation in all space. – Roger V. Sep 28 '21 at 04:38

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As soon as the electron meets the screen, you know its $x$ coordinate, so its $p$ is uncertain and so is its $y$ coordinate.

Vincent Thacker
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trula
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