Single Slit
V(x, y) = 8(abs(x) < 0.2) · (abs(y) > 0.5)
Open in the app The dials and keys named below are the app's.
What you see
The formula is the potential over the plane. abs(x) < 0.2 stands a wall 0.4 thick along the y axis, and abs(y) > 0.5 leaves one opening in it, 1 wide, on the axis. The 8 is the wall's height. The packet's energy is k₀²/2 + 1/2σ² = 4.5 + 0.5 = 5, below that, so the floor under the wall is tinted as ground it cannot classically enter.
The packet starts at (−4, 0) with Packet width 1 and Momentum k₀ (along x) 3. Its wavelength is 2π/k₀ ≈ 2.09, and it arrives at the wall about 1.3 seconds in at Speed 1.
The fan
The opening is 1 wide and the wave is 2.09 long, so the hole is half a wavelength across. A slit only casts a beam when it is many wavelengths wide. This one cannot, and what leaves it spreads into a fan tens of degrees wide, with most of the probability inside about 30° of the axis. Nor does it have dark lines of its own: the first would need sin θ = λ/a ≈ 2.09, and no angle gives that. The Double Slit preset next to it does have one, and gets it from the spacing of its two openings, not from their width. That is the difference worth carrying away: width spreads a wave, spacing makes fringes.
Where T settles
T settles near 0.75, which one opening in sixteen units of wall cannot explain. The wall is thin and only 8 tall against an energy of 5, so the wave decays inside it over 1/√(2(8 − 5)) ≈ 0.41 and much of the packet tunnels through the wall itself. Sealed, it still passes 0.55. What comes through the wall and what comes through the slit then interfere, adding structure that has nothing to do with the opening.
Try
- Change the 8 to 30. The wall goes opaque, T falls to about 0.48, and what is on the far side came through the slit and nowhere else.
- With the wall at 30, widen the opening to 30 · (abs(x) < 0.2) · (abs(y) > 1.5): three units across, and the fan narrows as T rises to about 0.83.
- Raise Momentum k₀ (along x) to 6: half the wavelength through the same hole, and the fan pulls in to a forward beam.
- Press Top for the plan view, which is where the width of the fan can be read off.