130_notes.dvi

Now let’s look at the (anti)symmetry of the statesof two identical electrons. For the ground
state, the spatial state is symmetric, so the spin state must be antisymmetric⇒s= 0.

u 0 =φ 100 φ 100

1

√

2

(χ+χ−−χ−χ+)

For excited states, we can make either symmetric or antisymmetricspace states.

u( 1 s)=

1

√

2

(φ 100 φ 2 ℓm+φ 2 ℓmφ 100 )

1

√

2

(χ+χ−−χ−χ+)

u( 1 t)=

1

√

2

(φ 100 φ 2 ℓm−φ 2 ℓmφ 100 )χ+χ+

The first state iss= 0 or spinsinglet. The second state iss= 1 or spintripletand has threems
states. Only the +1 state is shown.Because the large correction due to electron repulsion
is much larger for symmetric space states, the spin of the state determines the energy.

We label the states according to the spin quantum numbers, singletor triplet. We will treat V as a
perturbation. It is very large, so first order perturbation theory will be quite inaccurate.