Skip to main content
Physics

Return to Question

Bumped by Community user
added 5 characters in body; edited tags; edited title
Source Link
Qmechanic ♦
Qmechanic ♦
  • 212.9k
  • 48
  • 589
  • 2.3k

When creating term symbols, how do you know if the angular momentum L$L$ is antisymmetric of symmetric?

For example I'm trying to get the term symbol of $(1s)^{2}(2s)^{2}(2p)^2$ . In the answers they state the following:

The combination of angular momenta $L_1$ = $L_2$ = 1$L_1 = L_2 = 1$ gives L = 2$L = 2$ (symmetric), L = 1 $L = 1$ (antisymmetric) and L = 0$L = 0$ (symmetric). This must be combined with the spin spin wave function of opposite symmetry, thus $^1D_2, ^3P_{0, 1, 2}$ and $^1S_0.$

I totally understand this, except for how they assign symmetric and antisymmetric to the angular momenta. In the previous exercise I only had L = 0$L = 0$ and they said it was symmetric and antisymmetric. So how do I know if the angular momentum is symmetric or antisymmetric?

When creating term symbols, how do you know if the angular momentum L is antisymmetric of symmetric?

For example I'm trying to get the term symbol of $(1s)^{2}(2s)^{2}(2p)^2$ . In the answers they state the following:

The combination of angular momenta $L_1$ = $L_2$ = 1 gives L = 2 (symmetric), L = 1 (antisymmetric) and L = 0 (symmetric). This must be combined with the spin wave function of opposite symmetry, thus $^1D_2, ^3P_{0, 1, 2}$ and $^1S_0.$

I totally understand this, except for how they assign symmetric and antisymmetric to the angular momenta. In the previous exercise I only had L = 0 and they said it was symmetric and antisymmetric. So how do I know if the angular momentum is symmetric or antisymmetric?

When creating term symbols, how do you know if the angular momentum $L$ is antisymmetric of symmetric?

For example I'm trying to get the term symbol of $(1s)^{2}(2s)^{2}(2p)^2$ . In the answers they state the following:

The combination of angular momenta $L_1 = L_2 = 1$ gives $L = 2$ (symmetric), $L = 1$ (antisymmetric) and $L = 0$ (symmetric). This must be combined with the spin wave function of opposite symmetry, thus $^1D_2, ^3P_{0, 1, 2}$ and $^1S_0.$

I totally understand this, except for how they assign symmetric and antisymmetric to the angular momenta. In the previous exercise I only had $L = 0$ and they said it was symmetric and antisymmetric. So how do I know if the angular momentum is symmetric or antisymmetric?

edited tags
Link
SuperCiocia
SuperCiocia
  • 25.3k
  • 20
  • 90
  • 177
Source Link
Caspertijmen1
Caspertijmen1
  • 237
  • 1
  • 9

When creating term symbols, how do you know if the angular momentum L is antisymmetric of symmetric?

For example I'm trying to get the term symbol of $(1s)^{2}(2s)^{2}(2p)^2$ . In the answers they state the following:

The combination of angular momenta $L_1$ = $L_2$ = 1 gives L = 2 (symmetric), L = 1 (antisymmetric) and L = 0 (symmetric). This must be combined with the spin wave function of opposite symmetry, thus $^1D_2, ^3P_{0, 1, 2}$ and $^1S_0.$

I totally understand this, except for how they assign symmetric and antisymmetric to the angular momenta. In the previous exercise I only had L = 0 and they said it was symmetric and antisymmetric. So how do I know if the angular momentum is symmetric or antisymmetric?