Last Updated on May 31, 2025 by Dr. Sushanta Barman
Online Simulator
This simulator visualizes the quantum interference pattern from various slit gratings. Adjust parameters, then click “Run Simulation” and “Run Build-Up” to see how individual particle detections form the interference envelope.
Charge: C
Equations and Parameter Definitions
Single‐Slit Diffraction (N = 1):
\[I(y)\;\propto\;\bigl[\mathrm{sinc}\!\bigl(\pi\,a\,\tfrac{y}{\lambda\,L}\bigr)\bigr]^{2},\]
where, \(a\) is the slit width (in μm), \(\lambda\) is the de Broglie wavelength of the particle, \(L\) is the distance from the slit to the screen (in m or cm), and \(y\) is the vertical coordinate on the screen.
Double‐Slit Interference (N = 2):
\[I(y)\;\propto\;\cos^{2}\!\Bigl(\pi\,d\,\tfrac{y}{\lambda\,L}\Bigr)\;\times\;\bigl[\mathrm{sinc}\!\bigl(\pi\,a\,\tfrac{y}{\lambda\,L}\bigr)\bigr]^{2},\]
where, \(d\) is the center-to-center separation of the two slits (in μm), the \(\cos^{2}\) term determines the interference fringe spacing, and the \(\mathrm{sinc}^{2}\) term represents the diffraction envelope due to each individual slit.
Multi‐Slit Grating (N ≥ 2):
Let \(\displaystyle \phi = \pi\,d\,\frac{y}{\lambda\,L}.\) Then
\[I(y)\;\propto\;\Bigl[\tfrac{\sin\bigl(N\phi\bigr)}{\sin(\phi)}\Bigr]^{2}\;\times\;\bigl[\mathrm{sinc}\!\bigl(\pi\,a\,\tfrac{y}{\lambda\,L}\bigr)\bigr]^{2},\]
where, \(N\) is the total number of slits, the factor \(\left[\sin(N\phi)/\sin(\phi)\right]^2\) generates narrow principal maxima (bright fringes) due to multi-slit interference, and the \(\mathrm{sinc}^2\) envelope arises from single-slit diffraction of width \(a\).
Dr. Sushanta Barman is a Postdoctoral Fellow at the Tata Institute of Fundamental Research, working on quantum physics and matter-wave phenomena. Through MatterWaveX, he shares articles on modern physics, quantum technology, and scientific simulations.
