Recent content by arkajad

The old problem of large quantum numbers and the correspondence principle is still being discussed. Cabrera and Kiwi, Large quantum-number states and the correspondence principle, Phys. Rev. A 36, 2995(R) September 1987 show how it can be violated for the harmonic oscillator.

Happy end of the story: http://arxiv.org/abs/1502.03382']Asymptotic[/PLAIN] evaluation of an integral arising in quantum harmonic oscillator tunnelling probabilities R B Paris (Submitted on 11 Feb 2015)

This is not a measurement, because it does not result in an "event" that happens in final time. I know that it is hard to admit it, but that's life. The sooner experts realize it and state it clearly and aloud - the better will be chances to solve the measurement problem in quantum mechanics...

This is only partly true. Quantum theory does not have a dynamical scheme describing the process of "obtaining information".

But the basis e_i is a basis of column vectors, while the basis e^i is a basis of row vectors! Can you understand the difference between components of a vector and the index numbering basis vectors? It is important.

"Am I right in thinking though that a subscript usually indicates a row vector, and a superscript a column?" That's correct.

You wrote "I assumed them from the vector representation section". But there you must be careful. There are two different bases in this section. Unfortunately it is not clearly explained there what are these bases.

Where did you get these two formulas from? I do not see them at the quoted Wikipedia page.

The paper makes no sense at all as long as the concept of "measurement" is not precisely dynamically defined within quantum theory. These are just words with no precise meaning. Of course this what physicists do at the present time. Extraordinary claims need extraordinary proofs.

What you hear is one thing and what can be proved is another thing. Quantum theory does not have a formalism for dynamically describing "knowing." So, what you hear is what many people think, but are not able to prove. A proof would require a reliable and accepted unanomously "measurement...

Avodyne: Please check the new file . The paper is at the final stages. there is still an "anonymous helper" in the acknowledgments.

Update: computed 100 additional points. Plotted the asymptotic formula vs numerical "exact data". The agreement seems to be too good to be accidental and yet a solid mathematical foundation is still missing.

Thanks. Increasing the precision Mathematica was able to give a reasonable number also for n=612: 0.01575584. Perhaps I will now look for some help from expert mathematicians to be check if in this particular case the global asymptotic formula can be justified.

Avodyne, Since I did not see this problem discussed in depth anywhere, and since it seems to be interesting as it deals with the properties of one of the most fundamental models in quantum mechanics, perhaps you would like to write a short paper on this subject? These results should be available...

I agree. Yet there is till one unsolved problem. Wikipedia (following Szego) tells us that the error estimate in the Airy function approximation is valid for "t bounded". But we are using the formula for the unbounded region, extending to infinity. The results came out to be good, but a real...