00-383 A.A. Balinsky, W.D. Evans and Roger T. Lewis

On the Schr\"{o}dinger operator in $\mathbb{R}^2$ with an Aharonov-Bohm magnetic field (106K, "Postscript") Oct 2, 00

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Abstract. It is proved that the form domain of the magnetic Schr\"{o}dinger operator $S_A$ in $L^2 (\mathbb{R}^2)$ with an Aharonov-Bohm magnetic field is continuously embedded in $L^{\infty} (\mathbb{R}^+, \ rdr) \otimes L^2 (\mathbb{S}^1)$. An implication of this is that, when $V \in L^{1} (\mathbb{R}^+, \ rdr) \otimes L^{\infty} (\mathbb{S}^1) $, \ $S_A$ and $S_A +V$ have the same form domain and coincident essential spectrum, namely $[0, \infty)$

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