Abstract
We use a non-gauge-invariant modification of the exact Hamiltonian to obtain a new Hamiltonian-like operator for a simple exactly solvable boson model. The eigenvalues of the new operator are close to those of the original Hamiltonian. We make a one-body approximation of the new two-body operator in the spirit of the Bogoliubov approximation. Because only the number operator appears, the c-number approximation is not required individually for the creation or annihilation operators in the ground state. For the simple model, the results using the new approximation are closer to the exact results than the usual Bogoliubov results over a wide range of parameters. The improvement increases dramatically as the model interaction strength increases.
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Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 190, No. 1, pp. 124–137, January, 2017.
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Litt, O., Bassichis, W.H. A modified Bogoliubov method applied to a simple boson model. Theor Math Phys 190, 109–119 (2017). https://doi.org/10.1134/S0040577917010093
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DOI: https://doi.org/10.1134/S0040577917010093