Berry phase, Bra-Ket and gradient

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Discussion Overview

The discussion revolves around the derivation of an equation involving the curl of a vector expression that includes gradient and ket-bra notation. Participants seek clarity on the mathematical steps required to transition from one side of the equation to the other, with a focus on vector algebra in a three-dimensional space.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant requests a step-by-step derivation of an equation, indicating a need for clarity on the mathematical process involved.
  • Another participant expresses confusion regarding the notation used, suggesting that more context is necessary to understand the discussion.
  • A participant mentions the need to solve a curl involving gradient and ket-bra vectors, asserting it is a matter of elementary vector algebra.
  • Concerns are raised about the meaning of a cross product between a ket and a bra, highlighting the need for clear definitions and context.
  • A participant queries the origin of the equation in question, seeking additional information or references.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus, as there are multiple competing views regarding the notation and the mathematical concepts involved. The discussion remains unresolved with respect to the clarity of the equation and the steps needed for its derivation.

Contextual Notes

Limitations include the lack of clear definitions for the notation used, assumptions about the mathematical framework, and the specific context in which the equation is applied.

Lucy166
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Could somebody show me how to derive this equation? How can I get right side from left. Step by step, thanks...
ASxbBF2.png
 

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I've no clue, what your notation means. We need more context!
 
I only want to know how to solve this curl in left side when I have gradient and ket-bra vectors. I suppose it is elementary vector algebra. It’s simply a math. I need to show that solution of this curl is right side of this equation in this form.

R (external variables) is set of parameters (R1, R2, R3…). In this section, for sake of simplicity, the parameter space R is assumed to span an ordinary three dimensional space. We don’t need generalization of vector algebra to a multi-dimensional space. ∂/∂R=∇R. We consider eigenfunctions psi. Internal variables of the system are collectively indicated by r.
 
Then it's even more puzzling. What should a cross product between a ket and a bra mean? Again, we need the context and a clear definition of your notation!
 
Lucy166 said:
this equation?

Where does this equation come from?
 

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