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Higher conservation laws for the quantum non-linear Schrödinger equation

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  • Davies, B.

Abstract

We construct explicit forms for two non-trivial conservation laws of the quantum non-linear Schrödinger equation and show that they have the correct quasi-classical limit. For H4 the second quantised form cannot be obtained by normal ordering of the classical conserved quantity H4cl. We show the quantum inverse scattering method also gives the correct higher Hamiltonians H3 and H4. The surprising result is that the expansion of fundamental integrals of motion such as A(λ), in inverse powers of λ, cannot be recovered by normal ordering of the classical expansion.

Suggested Citation

  • Davies, B., 1990. "Higher conservation laws for the quantum non-linear Schrödinger equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 167(2), pages 433-456.
    • Handle: RePEc:eee:phsmap:v:167:y:1990:i:2:p:433-456
    DOI: 10.1016/0378-4371(90)90126-D
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