Understanding Circumflex Operators: Get Help Now

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Discussion Overview

The discussion revolves around understanding the difference between circumflex operators (notated as Ĥ) and non-circumflex operators (notated as H), particularly in the context of quantum mechanics. Participants seek clarification on the meaning and implications of normalization in this context.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • Some participants express confusion about the distinction between circumflex operators and non-circumflex operators, specifically regarding the term "normalized."
  • One participant mentions that their physics teacher stated that the circumflex operator is normalized, but they do not understand the implications of this normalization.
  • Another participant questions whether the teacher provided examples of normalized versus non-normalized operators to clarify the distinction.
  • Some participants note that the notation of circumflex operators is not commonly discussed and express uncertainty about what "normalization of an operator" entails.
  • There is a request for references or sources that explain these distinctions, indicating a need for more information on the topic.

Areas of Agreement / Disagreement

Participants generally agree that there is confusion surrounding the terms and concepts related to circumflex operators and normalization. Multiple competing views and uncertainties remain regarding the definitions and implications of these terms.

Contextual Notes

Limitations include a lack of clear definitions for "normalization" in this context, absence of examples illustrating the differences between normalized and non-normalized operators, and the need for references to support the discussion.

regory
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Hi
I have a problem for understanding the difference between an circumflex operator and non-circumflex operador.
I'd appreciate your help
 
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regory said:
I have a problem for understanding the difference between an circumflex operator and non-circumflex operador.

Where are you seeing these terms used? Can you give a reference?
 
Today my physics teacher said that the circumflex operator (for example Ĥ) is different to the operator H because Ĥ is normalized. I have always used ^ for denote any operator and I don't find information about this difference.
 
regory said:
my physics teacher said that the circumflex operator (for example Ĥ) is different to the operator H because Ĥ is normalized.

Did you ask your teacher what they meant by "normalized", or what difference "normalizing" an operator makes?

regory said:
I don't find information about this difference.

Where have you looked?
 
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PeterDonis said:
Did you ask your teacher what they meant by "normalized", or what difference "normalizing" an operator makes?

Or, did your teacher give explicit examples of a non-normalized operator ##H## and the corresponding normalized operator ##\hat{H}##?
 
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I think we'd need a source, where these distinctions are made. It's not a common notation. Usually one uses a hat above a symbol to indicate that one deals with an operator rather than a (real or complex) number in quantum mechanics. I also don't know, what "normalization of an operator" means.
 

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