Harmonic oscillators in relativistic quantum mechanics |
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| Authors: | Jacek Karwowski Grzegorz Pestka |
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| Affiliation: | (1) Instytut Fizyki, Uniwersytet Mikołaja Kopernika, ul. Grudzia̧dzka 5, 87-100 Toruń, Poland |
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| Abstract: | Relativistic generalisations of the harmonic oscillator are analysed. Lévy–Leblond, Dirac and Klein–Gordon equations which in the limit of a non-relativistic and spinless particle transform into Schrödinger equation for the harmonic oscillator are constructed. Properties of their solutions, in particular the structure of their spectra, are analysed. Applications to modelling phenomena relevant in quantum chemistry are briefly discussed. |
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| Keywords: | Harmonic oscillator Schr?dinger equation Klein– Gordon equation Dirac equation Lévy– Leblond equation |
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