Poetry of Physics and the Physics of Poetry

Wave Mechanics 201

slit open but receive no electrons with both slits open. Only a
probabilistic description allows us to understand how electron diffraction
takes place.

Wave Mechanics 193

electrons with both slits open. Only a probabilistic description allows us

to understand how electron diffraction takes place.

Fig 20.2 (a) |$ 1 |^2 +^ |$ 2 |^2 Fig 20.2 (b) |($ 1 + $ 2 )|^2

Wave Packets

De Broglie was the first to indicate the wave-like properties of the

electron, which explains the diffraction behaviour described above. De

Broglie assigned to the electron a single wavelength! related to its

momentum p by! = h/p. We have learned, however, in our discussion of

the uncertainty principle that a particle rarely has a precisely defined

momentum. We therefore expect the wave function describing the

particle to be composed of many waves, each with a different

wavelength. Such a superposition of waves is called a wave packet. Let

us consider a wave packet composed of several waves with wavelengths

between! and! + #!. The momentum of these waves and hence the

particle is spread out between h/! and h/(! + #!). The uncertainty in the

momentum of the particle is therefore approximately #p = h/! – h/(! +

#! ) = h #!/!^2.

The size of the wave packet describing an atomic particle increases

with time. This does not mean that the actual size of the particle

increases. It remains the same but the wave packet and hence, the

uncertainty in the particles position does increase with time. The reason

for this is that the different waves in the packet are traveling at different

Fig. 20.2(a) |ψ 1 |^2 +^ |ψ 2 |^2

Wave Mechanics 193

electrons with both slits open. Only a probabilistic description allows us

to understand how electron diffraction takes place.

Fig 20.2 (a) |$ 1 |^2 +^ |$ 2 |^2 Fig 20.2 (b) |($ 1 + $ 2 )|^2

Wave Packets

De Broglie was the first to indicate the wave-like properties of the

electron, which explains the diffraction behaviour described above. De

Broglie assigned to the electron a single wavelength! related to its

momentum p by! = h/p. We have learned, however, in our discussion of

the uncertainty principle that a particle rarely has a precisely defined

momentum. We therefore expect the wave function describing the

particle to be composed of many waves, each with a different

wavelength. Such a superposition of waves is called a wave packet. Let

us consider a wave packet composed of several waves with wavelengths

between! and! + #!. The momentum of these waves and hence the

particle is spread out between h/! and h/(! + #!). The uncertainty in the

momentum of the particle is therefore approximately #p = h/! – h/(! +

#! ) = h #!/!^2.

The size of the wave packet describing an atomic particle increases

with time. This does not mean that the actual size of the particle

increases. It remains the same but the wave packet and hence, the

uncertainty in the particles position does increase with time. The reason

for this is that the different waves in the packet are traveling at different

Fig. 20.2(b) |(ψ 1 + ψ 2 )|^2

Wave Packets

De Broglie was the first to indicate the wave-like properties of the
electron, which explains the diffraction behaviour described above.
De Broglie assigned to the electron a single wavelength λ related to its
momentum p by λ = h/p. We have learned, however, in our discussion
of the uncertainty principle that a particle rarely has a precisely
defined momentum. We therefore expect the wave function describing
the particle to be composed of many waves, each with a different
wavelength. Such a superposition of waves is called a wave packet. Let
us consider a wave packet composed of several waves with wavelengths
between λ and λ + ∆λ. The momentum of these waves and hence the
particle is spread out between h/λ and h/(λ + ∆λ). The uncertainty in
the momentum of the particle is therefore approximately ∆p = h/λ –
h/(λ + ∆λ) = h ∆λ/λ^2.
The size of the wave packet describing an atomic particle increases
with time. This does not mean that the actual size of the particle
increases. It remains the same but the wave packet and hence, the
uncertainty in the particles position does increase with time. The reason
for this is that the different waves in the packet are traveling at different
speeds because of their spread in momentum. The waves with
momentum p + ∆p gets ahead of the waves with momentum p and