Understanding Circumflex Operators: Get Help Now

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SUMMARY

The discussion centers on the distinction between circumflex operators, specifically the normalized operator denoted as Ĥ, and non-circumflex operators such as H. A key point raised is that the circumflex operator indicates normalization, which is a concept not commonly understood or referenced in available literature. Participants emphasize the need for explicit examples and sources to clarify the differences and applications of these operators in quantum mechanics.

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  • Knowledge of normalization concepts in mathematical contexts
  • Basic grasp of the differences between real and complex numbers
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Students of physics, particularly those studying quantum mechanics, educators seeking to clarify operator notation, and anyone interested in the mathematical foundations of quantum theory.

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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