NDLI: Quantum and Classical Disparity and Accord

Content Provider	Springer Nature Link
Author	Rabiwitz, Mario
Copyright Year	2008
Abstract	Discrepancies and accords between quantum (QM) and classical mechanics (CM) related to expectation values and periods are generally found for both the harmonic oscillator (SHO) and a free particle in a box (FPB), which may apply generally. These indicate non-locality is expected throughout QM. The FPB energy states violate the Correspondence Principle. Previously unexpected accords are found and proven that 〈x $^{2}$〉$_{ CM }$=〈x $^{2}$〉$_{ QM }$ and τ $_{ CM }$=τ $_{ QMb }$ (beat period i.e. beats between the phases for adjoining energy states) for the SHO for all quantum numbers, n. However, for the FPB the beat periods differ at small n. It is shown that a particle’s velocity in an infinite square well varies, no matter how wide the box, nor how far the particle is from the walls. The quantum free particle variances share an indirect commonality with the Aharonov-Bohm and Aharonov-Casher effects in that there is a quantum action in the absence of a force. The concept of an “Expectation Value over a Partial Well Width” is introduced. This paper raises the question as to whether these inconsistencies are undetectable, or can be empirically ascertained. These inherent variances may need to be fixed, or nature is manifestly more non-classical than expected.
Starting Page	706
Ending Page	722
Page Count	17
File Format	PDF
ISSN	00207748
Journal	International Journal of Theoretical Physics
Volume Number	48
Issue Number	3
e-ISSN	15729575
Language	English
Publisher	Springer US
Publisher Date	2008-09-23
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Harmonic oscillator and free particle expectation values Non-locality Aharonov-Bohm and Aharonov-Casher effects Newton’s first and second laws in quantum mechanics Expectation values over complete and partial intervals Correspondence Principle violation Mathematical and Computational Physics Elementary Particles, Quantum Field Theory Quantum Physics Physics
Content Type	Text
Resource Type	Article
Subject	Physics and Astronomy Mathematics

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
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3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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