Matrix representation of the time operator
- Department of Physics, Kings College London, Strand, London WC2R 1LS (United Kingdom)
- Dipartimento di Matematica e Fisica, Universita del Salento and I.N.F.N. Sezione di Lecce, Via Arnesano, I-73100 Lecce (Italy)
In quantum mechanics the time operator {Theta} satisfies the commutation relation [{Theta}, H]=i, and thus it may be thought of as being formally canonically conjugate to the Hamiltonian H. The time operator associated with a given Hamiltonian H is not unique because one can replace {Theta} by {Theta}+{Theta}{sub hom}, where {Theta}{sub hom} satisfies the homogeneous condition [{Theta}{sub hom}, H]= 0. To study this nonuniqueness the matrix elements of {Theta} for the harmonic-oscillator Hamiltonian are calculated in the eigenstate basis. This calculation requires the summation of divergent series, and the summation is accomplished by using zeta-summation techniques. It is shown that by including appropriate homogeneous contributions, the matrix elements of {Theta} simplify dramatically. However, it is still not clear whether there is an optimally simple representation of the time operator.
- OSTI ID:
- 22093610
- Journal Information:
- Journal of Mathematical Physics, Vol. 53, Issue 6; Other Information: (c) 2012 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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