Hydrogen part II

L = 0 there is only one state since it is a
sphere

l= 1 there are three states but it depends
on the orientation (superposition of 3 states)

L = 2 there are 5 states that get
superimposed

L = (2l + 1

You should make it complex

x=rsin#cos$

y=rsin#cos$

z= rcos#

Group-
things that you can do, combined you get a rotation (5 + 10 = 15 degrees)

Rotations
don’t commute

One
rotation times the second isnt always the same depending on the order

1925.
Electron spin

Found
the 2 state

Can
be spin up or spin down

If
it is spin up, then there is a probability for it to be spin up or spin down

Pauli
would rock on his chair so the experiments don’t work

The
Pauli affect

1926.
Wave functions

L
= 0 and spin 1/2

(1/2
because you want to get the even numbers for l)

Electron
in orbit has a magnetic moment proportional to l and the spin

So
its related to the angular momentum

Classical
vs. quantum for angular momentum

L
= 0 X spin 1/2 = 1/2

L
= 1 X spin 1/2 = 6 states but only two of them linearly combine

=
split into 2 states and four states

1/2
+ 3/2

L
= 2 X spin 1/2 = 3/2 + 5/2

1932.
Neutron was found

1936.
Nuclear fission

They
didn’t go any farther in atomic level because we had the Dirac theory

But
anytime you squared the field it would be infinity

It
was found through experiment that 2s 1/2 was less energy than 2p 1/2

They
are separated by 1057 MHz and this is called the Lamb shift

This
went against Dirac's theory that they were equal

1947.
Relativistic equations were made in
America but also in Japan

21
cm line

The
proton also spins

Learn
about structure of galaxy

So
the electron can be spin up or down

The
proton can be spin up or down too