How does parity transformation affect Bloch states?

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SUMMARY

Parity transformation in quantum mechanics directly affects Bloch states by inverting the Bloch wave vector. Specifically, when a parity transformation is applied, the Bloch state vector transforms according to the relation k → -k, where k represents the Bloch wave vector. This transformation is crucial for understanding the symmetry properties of quantum states in periodic potentials. The discussion highlights the need for a formal proof of this transformation, which can be derived through mathematical substitution in the Bloch state representation.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with Bloch states and wave vectors
  • Knowledge of parity transformation in odd-dimensional spaces
  • Basic mathematical skills for vector manipulation
NEXT STEPS
  • Research the mathematical proof of Bloch state transformation under parity
  • Explore the implications of parity transformation on electronic band structure
  • Study the role of symmetry in quantum mechanics
  • Learn about applications of Bloch states in solid-state physics
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Quantum physicists, solid-state physicists, and students studying the effects of symmetry in quantum systems will benefit from this discussion.

Joker93
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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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Plug and chug, write out a Bloch state vector and substitute...in my head it works out pretty quickly
 

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