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wdlang
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it is a well known result, but it is a rigorious result or not?
tom.stoer said:You mean Anderson localization?
genneth said:In 1D, yes, it is fully rigorous. A quick google brings up references and papers --- too many to list here.
jostpuur said:I don't believe this. Even the Bloch's theorem is not dealt with rigorously, so how could the Anderson localization then? The Anderson localization looks like more complicated phenomenon than Bloch waves.
No, the well-known result may not always be considered rigorous. It depends on the specific situation and context in which the result is being applied.
The factors that determine if a well-known result is rigorous include the validity of the assumptions and the soundness of the logical reasoning used to arrive at the result.
Yes, a result can be well-known but not rigorous. This could be due to a lack of evidence or proof to support the result, or because the result has been widely accepted without being thoroughly tested.
Rigorous proof is essential for a result to be considered valid and reliable. Without rigorous proof, the result may be based on flawed assumptions or faulty reasoning, leading to incorrect conclusions.
Yes, scientists always strive for rigorous results. The scientific method is based on rigorous testing and validation of hypotheses, and scientists are constantly working to improve and refine their methods to ensure the rigor of their results.