Operators of the quantum harmonic oscillator and its relatives

Szafraniec, Franciszek Hugon

doi:10.1002/9781118855300.ch2

Cited by 2 publications

(2 citation statements)

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“…The example we have in mind is a symmetric operator and selfadjoint as well, in which case the domain makes the difference (cf. [15] or for much more particularities also [27]). This is invisible when the notion of a Hermitian operator is the only one in use, with a consequence of an automatic transplantation of the † operation from finite matrices together with its algebraic properties to would-be Hilbert space operators.…”

Section: Discussionmentioning

confidence: 99%

“…Summing up, though, our main goal has been to prove rigorously the impossibility of generalizing squeezing to higher orders in a naive way; one of the benefits of our investigations is to call reader's attention to a need of being aware how important and helpful a domain is for studying properties of a specific operator; for a thorough discussion of the issue the chapter [27] is highly recommended.…”

Section: Discussionmentioning

confidence: 99%

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Squeezing of arbitrary order: the ups and downs

2014

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We show how using classical von Neumann index theory makes possible a universal treatment of squeezing of arbitrary order. 'Universal' means that the same approach applied to displacement (order 1) and squeeze (order 2) operators confirms firmly and unequivocally what is already known as well as provides rigorous arguments that the higher order squeezing cannot be generalized in a 'naive' way. We create an environment for answering definitely all the emerging questions in positive (the ups) and negative (downs). In the latter case, we suggest ways for further development.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Squeezing of arbitrary order: the ups and downs

2014

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Symmetrized exponential oscillator

Znojil

2016

Mod. Phys. Lett. A

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Several properties of bound states in potential V (x) = g 2 exp(|x|) are studied. Firstly, with the emphasis on the reliability of our arbitrary-precision construction, wave functions are considered in the two alternative (viz., asymptotically decreasing or regular) exact Bessel-function forms which obey the asymptotic or matching conditions, respectively. The merits of the resulting complementary transcendental secular equation approaches are compared and their applicability is discussed.

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Operators of the quantum harmonic oscillator and its relatives

Cited by 2 publications

References 61 publications

Squeezing of arbitrary order: the ups and downs

Squeezing of arbitrary order: the ups and downs

Symmetrized exponential oscillator

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