Is Complex Scaling in Quantum Mechanics Fully Understood?

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SUMMARY

Complex scaling in quantum mechanics is a method used to analyze the eigenfunctions of the complex scaled Hamiltonian, which are believed to form a complete basis set. The theoretical foundation of this method is well-established through the Aguilar-Balslev-Combes (ABC) theorem, published in 1971 in the journal Communications in Mathematical Physics. Access to the original article may be restricted, but understanding the mathematical arguments behind complex scaling is essential for grasping its implications in quantum mechanics.

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Quantum River
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Could anyone tell me what complex scaling is?

Do the eigenfunctions of the complex scaled Hamiltonian form a complete basis set? Some articles say the theoretical basis of the complex scaling method has been understood well by the ABC (Aguilar-Balslev-Combes) theorem. But the ABC article of these three guys is in Commun. Math. Phys. of 1971 year (I could not get access to springerlink.com).

I am aware of that this kind of technical problems should not be brought out here. But I just could not understand this method well. Could anyone give me a simple mathematical argument why the complex scaled basis set is complete? (Or give me some internet link that prove its mathematical basis.) The help will be greatly appreciated.

Thanks!

Quantum River
 
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Hi there - try the tutors at Brainmass.com. Very reasonable and have helped me out a lot. Lots of practise material in their library too.

LOL
 

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