Higher-order nonlocal approach to classical and quantum mechanics through non-standard Lagrangians: The case of quantum wells and the quantum states of neutron in earth's gravitational field

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60077344%3A_____%2F24%3A00616796" target="_blank" >RIV/60077344:_____/24:00616796 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1142/S0217732324500548" target="_blank" >https://doi.org/10.1142/S0217732324500548</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/S0217732324500548" target="_blank" >10.1142/S0217732324500548</a>

Result language

angličtina

Original language name

Higher-order nonlocal approach to classical and quantum mechanics through non-standard Lagrangians: The case of quantum wells and the quantum states of neutron in earth's gravitational field

Original language description

It is well-known that any dynamical system governed by a differential equation containing time derivatives higher than second order unavoidably holds unbounded energy solutions, dubbed ghosts that appear in the Hamiltonian. They correspond to instabilities displayed at the classical level. In this study, we show first that it is possible to construct in classical mechanics, characterized by non-standard Lagrangians and nonlocal-in-time kinetic energy, higher-order derivative theories that avoid the Ostrogradsky ghost. Second, we show that in the realm of quantum mechanics, higher-order discretized energies emerge in the theory which may lead to extended quantum mechanics formalism. The problem of quantum wells has been treated where we showed that negative energy and negative action, complexified energies and complexified actions may emerge in our formalism. We have also discussed the quantum motion of a neutron in the Earth's gravitational field. It was observed that within the realm of higher-order non-standard Lagrangians, the quantum energies of the neutrons are higher than the energy levels obtained in the basic formalism.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10102 - Applied mathematics

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2024

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Modern Physics Letters A

ISSN

0217-7323

e-ISSN

1793-6632

Volume of the periodical

39

Issue of the periodical within the volume

13

Country of publishing house

SG - SINGAPORE

Number of pages

25

Pages from-to

2450054

UT code for WoS article

001236180600002

EID of the result in the Scopus database

2-s2.0-85193960966