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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Modern Physics Letters A

ISSN

0217-7323

e-ISSN

1793-6632

Svazek periodika

39

Číslo periodika v rámci svazku

13

Stát vydavatele periodika

SG - Singapurská republika

Počet stran výsledku

25

Strana od-do

2450054

Kód UT WoS článku

001236180600002

EID výsledku v databázi Scopus

2-s2.0-85193960966