130_notes.dvi

5.7.3 The Dirac Delta Function Wave Packet*

Given the following one dimensional probability amplitude in the position variable x, compute the
probability distribution in momentum space. Show that the uncertainty principle is roughly satisfied.
ψ(x) =δ(x−x 0 )

5.7.4 Can I “See” inside an Atom

To see inside an atom, we must use light with a wavelength smaller than the size of the atom. With
normal light, once a surface is polished down to the .25 micron level, it looks shiny. You can no
longer see defects. So to see inside the atom, we would need light withλ=hp= 0. 1 ̊A.

p =

2 π ̄h

0. 1

pc =

2 π ̄hc

0. 1

=

2 π 1973

0. 1

= 120000 eV

This is more than enough kinetic energy to blow the atom apart. You can’t “see” inside.

A similar calculation can be made with the uncertainty principle.

∆p∆x≥

̄h

2

∆(pc)∆x≥

̄hc

2

∆Eγ≥

̄hc

2∆x

Eγ≥

̄hc

2(0. 1 ̊A)

= 10000eV

The binding energy is 13 eV, so this will still blow it apart.

So we can’t “watch” the inside of an atom.

We can probe atoms with high energy photons (for example). Thesewill blow the atoms apart, but
we can use many atoms of the same kind. We learn about the internalstructure of the atoms by
scattering particles off them, blowing them apart.

5.7.5 Can I “See” inside a Nucleus

In a similar fashion to the previous section,Eγ≥2(0hc ̄. 1 F)= 1000 MeV.
The binding energy per nucleon is a few MeV, so, we will also blow nuclei apart to look carefully
inside them. We again can just use lots of nuclei to allow us to learn about internal nuclear structure.