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Trace formulas for the Schrödinger operator. (English) Zbl 0802.34089

The present paper provides a new derivation of the trace formula for one- and two-dimensional Schrödinger operators with periodic potential, i.e. a representation of the potential in terms of Dirichlet, Neumann, periodic, and antiperiodic eigenvalues in the one-dimensional case. While the one-dimensional results in this paper were known, they are derived by means of a new deformation argument. Moreover, the two-dimensional trace formula appears to be without precedent.

MSC:

34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
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References:

[1] Flaschka, Arch. Rat. Mech. Anal. 59 pp 293– (1975)
[2] Gesztesy, Bull. AMS 29 pp 250– (1993)
[3] McKean, Invent. Math. 30 pp 217– (1975)
[4] Trubowitz, Comm. Pure Appl. Math. 30 pp 321– (1977)
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