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Classically equivalent Hamiltonians and ambiguities of quantization: A particle in a magnetic field

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Il Nuovo Cimento B (1971-1996)

Summary

New Hamiltonians yielding classical equations of motion for a charged particle in a uniform magnetic field are found. It is shown esplicitly that, after canonical quantization, the new Hamiltonians describe different quantum systems which have nothing in common with the usual quantum particle in a magnetic field, because the spectra and measurability properties of the same conserved observables (kinetic energy, generalized angular momentum, etc.) for each system are quite different. The solutions and propagators of the Schrödinger equation with the new Hamiltonians are obtained.

Riassunto

Si trovano nuove hamiltoniane che danno equazioni di moto classiche per una particella carica in un campo magnetico uniforme. Si mostra esplicitamente che, secondo la quantizzazione canonica, le nuove hamiltoniane descrivono sistemi quantici diversi che non hanno niente in comune con la particella quantica, usuale in un campo magnetico, perchè lo spettro e le proprietà di misurabilità delle stesse osservabili conservate (energia cinetica, impulso angolare generalizzato, ecc.) per ciascun sistema sono diverse. Si ottengono soluzioni e propagatori dell’equazione di Schrödinger con nuove hamiltoniane.

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Authors and Affiliations

  1. P. N. Lebedev Physical Institute, Leninsky Prospekt, 53, 117924, Moscow, USSR

    V. V. Dodonov, V. I. Man’ko & V. D. Skarzhinsky

Authors
  1. V. V. Dodonov
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  2. V. I. Man’ko
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  3. V. D. Skarzhinsky
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Dodonov, V.V., Man’ko, V.I. & Skarzhinsky, V.D. Classically equivalent Hamiltonians and ambiguities of quantization: A particle in a magnetic field. Nuov Cim B 69, 185–205 (1982). https://doi.org/10.1007/BF02721265

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