Chapter 27.2, Problem 32SSC

To determine

The way Heisenberg’s uncertainty principle explains the interference pattern formed when one atom or a photon passes through slits.

Explanation of Solution

Introduction:

According to Heisenberg uncertainty principle:

  $\Delta x.\Delta p\ge \frac{h}{4\pi }$

The error in calculating position and momentum at a time p will be always greater than $\frac{h}{4\pi }$ .

In real life $\Delta x$ and $\Delta p$ are comparatively large with $\frac{h}{4\pi }$ for large bodies.

The interference pattern forms when a beam of light or atoms passes through two slits. As per uncertainty principle, if one tries to determine through which slit, the photon or atom passes through, then interreference is not formed.

If one photon or atom passes through the slits in double-slit experiment, interreference pattern can be obtained on the screen. One photon or atom interferes with itself. The wavefunction of the atom or photon can be obtained at both the slits which indicates that both exhibit wave nature in the double slit experiment.