## Why the total wave function is antisymmetric?

8.5: Wavefunctions must be Antisymmetric to Interchange of any Two Electrons. Quantum mechanics allows us to predict the results of experiments. If we conduct an experiment with indistinguishable particles a correct quantum description cannot allow anything which distinguishes between them.

## What is antisymmetric principle?

The postulate that electrons must be described by wavefunctions which are antisymmetric with respect to interchange of the coordinates (including spin) of a pair of electrons.

**Why is wave function antisymmetric for fermion?**

Identical boson wave functions must be symmetric under the interchange of any two particles. Hence, identical bosons can occupy the same quantum state. Identical fermion wave functions must be antisymmetric under interchange of particles, and therefore, fermions cannot occupy the same state.

### Are fermions symmetric or antisymmetric?

Fermions. A state of N fermions must be antisymmetric under every possible exchange operator: ˆPij|ψ⟩=−|ψ⟩∀i,j∈{1,…,N},i≠j. Similar to the bosonic case, we can explicitly construct multi-fermion states based on the occupancy of single-particle state.

### Why is singlet state antisymmetric?

Because the singlet state has spin 0, so the two particles that sum to 0 must be in states that are the opposite of each other.

**How do you know if a function is antisymmetric?**

In set theory, the relation R is said to be antisymmetric on a set A, if xRy and yRx hold when x = y. Or it can be defined as, relation R is antisymmetric if either (x,y)∉R or (y,x)∉R whenever x ≠ y. A relation R is not antisymmetric if there exist x,y∈A such that (x,y) ∈ R and (y,x) ∈ R but x ≠ y.

## How do you calculate Antisymmetric relations?

For anti-symmetric relation, if (a,b) and (b,a) is present in relation R, then a = b. (That means a is in relation with itself for any a). So for (a,a), total number of ordered pairs = n and total number of relation = 2n.

## Are triplet states antisymmetric?

Always the complete wave function of the two electron state has to be antisymmetric; consequently the ”local” wave function of a singlet state must be symmetric and for a triplet state it has to be antisymmetric.

**What is anti-symmetric relation with example?**

An example of antisymmetric is: for a relation “is divisible by” which is the relation for ordered pairs in the set of integers. For relation, R, an ordered pair (x,y) can be found where x and y are whole numbers and x is divisible by y.

### Are all Antisymmetric relations symmetric?

Some notes on Symmetric and Antisymmetric: • A relation can be both symmetric and antisymmetric. A relation can be neither symmetric nor antisymmetric.

### Is singlet state antisymmetric?

Thus the singlet state is antisymmetric and the triplet state is symmetric when exchanging the indices. Always the complete wave function of the two electron state has to be antisymmetric; consequently the ”local” wave function of a singlet state must be symmetric and for a triplet state it has to be antisymmetric.

**Why is the triplet state symmetric?**

The triplet spin state is symmetric, so that must be combined with an anti-symmetric spatial wavefunction. The singlet spin state, on the other hand, is anti-symmetric, so it must be combined with a symmetric spatial wavefunction in order for the overall state of the system to be anti-symmetric.