Class of Nonanalytic Perturbations in Quantum Mechanics
- 1 May 1967
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 8 (5) , 1121-1127
- https://doi.org/10.1063/1.1705326
Abstract
It is shown that the resolvent operator for the Hamiltonian which is the sum of the harmonic oscillator Hamiltonian H0 and a polynomial perturbation gP(x) of degree exceeding two (g is a coupling constant) is not expressible as a convergent power series in g. The source of this nonanalyticity is the failure of the anharmonic perturbation operator to be small in norm compared to H0. The nature of the singularity at g = 0 is conjectured. The result makes clear that the divergence of the Ward‐Hurst‐Thirring model has nothing to do with the ``difficulties'' of field theory which are related to the infinite number of degrees of freedom of a field.Keywords
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