How does parity transformation affect Bloch states?

In summary, under a parity transformation, the energy of Bloch states remains unchanged and the wavefunction may change sign, but its overall shape and structure remains the same. Parity transformation does not affect the momentum of Bloch states and cannot change their symmetry. The parity transformation operator acts on Bloch states by flipping the sign of the spatial coordinates.
  • #1
Joker93
504
36
Hello!
I want to know how does a parity transformation affect Bloch states! I always knew that parity takes the position vector to minus itself (in odd number of dimensions), but I have read that it also takes the Bloch wave vector to minus itself but I have not found a satisfactory proof of this.
Thank you.
 
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  • #2
Plug and chug, write out a Bloch state vector and substitute...in my head it works out pretty quickly
 

1. How does a parity transformation affect the energy of Bloch states?

Under a parity transformation, the energy of Bloch states remains unchanged. This is because parity is a symmetry operation that does not affect the underlying Hamiltonian or energy levels.

2. What happens to the wavefunction of a Bloch state under a parity transformation?

Under a parity transformation, the wavefunction of a Bloch state may change sign, but its overall shape and structure remain the same. This is because parity only affects the spatial coordinates and not the intrinsic properties of the wavefunction.

3. How does parity transformation affect the momentum of Bloch states?

Parity transformation does not affect the momentum of Bloch states. This is because momentum is a conserved quantity and is independent of the coordinate system used.

4. Can a parity transformation change the symmetry of Bloch states?

No, a parity transformation cannot change the symmetry of Bloch states. This is because parity is a symmetry operation itself and cannot alter the underlying symmetry properties of a system.

5. How does the parity transformation operator act on Bloch states?

The parity transformation operator acts on Bloch states by flipping the sign of the spatial coordinates. In mathematical terms, it can be represented as PΨ(x) = Ψ(-x), where P is the parity operator and Ψ is the wavefunction of the Bloch state.

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