Page 32 - PRINCIPLES OF QUANTUM MECHANICS as Applied to Chemistry and Chemical Physics

1.6 Young's double-slit experiment 23

The time Ät for a wave packet to pass a given point equals the uncertainty in
its position x divided by the group velocity v g
Äx Äx m
Ät ˆ ˆ ˆ Äx (1:47)
v g v p
Combining equations (1.46) and (1.47), we see that ÄEÄt ˆ ÄxÄp. Thus, the
relation (1.45) follows from (1.44). The Heisenberg uncertainty relation (1.45)
is treated more thoroughly in Section 3.10.

1.6 Young's double-slit experiment
The essential features of the particle±wave duality are clearly illustrated by
Young's double-slit experiment. In order to explain all of the observations of
this experiment, light must be regarded as having both wave-like and particle-
like properties. Similar experiments on electrons indicate that they too possess
both particle-like and wave-like characteristics. The consideration of the
È
experimental results leads directly to a physical interpretation of Schrodinger's
wave function, which is presented in Section 1.8.
The experimental apparatus is illustrated schematically in Figure 1.8. Mono-
chromatic light emitted from the point source S is focused by a lens L onto a
detection or observation screen D. Between L and D is an opaque screen with
two closely spaced slits A and B, each of which may be independently opened
or closed.
A monochromatic light beam from S passing through the opaque screen with
slit A open and slit B closed gives a diffraction pattern on D with an intensity
distribution I A as shown in Figure 1.9(a). In that ®gure the points A and B are
directly in line with slits A and B, respectively. If slit A is closed and slit B
open, the intensity distribution of the diffraction pattern is given by the curve
labeled I B in Figure 1.9(a). For an experiment in which slit A is open and slit
B is closed half of the time, while slit A is closed and slit B is open the other
half of the time, the resulting intensity distribution is the sum of I A and I B ,as
shown in Figure 1.9(b). However, when both slits are open throughout an

D
L A

S
B

Figure 1.8 Diagram of Young's double-slit experiment.