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Higher conservation laws for the quantum non-linear Schrödinger equation

✍ Scribed by B. Davies

Publisher
Elsevier Science
Year
1990
Tongue
English
Weight
959 KB
Volume
167
Category
Article
ISSN
0378-4371

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✦ Synopsis

We construct explicit forms for two non-trivial conservation laws of the quantum non-linear Schrrdinger equation and show that they have the correct quasi-classical limit. For //4 the second quantised form cannot be obtained by normal ordering of the classical conserved quantity H4 ~. We show that the quantum inverse scattering method also gives the correct higher Hamiltonians H3 and H 4. The surprising result is that the expansion of fundamental integrals of motion such as A(A), in inverse powers of A, cannot be recovered by normal ordering of the classical expansion.

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