Multi-dimensional Schrödinger operators with some negative spectrum
نویسندگان
چکیده
منابع مشابه
Multi-dimensional Schrödinger Operators with Some Negative Spectrum
In this paper we consider Schrödinger operators −∆+ V (x), V ∈ L∞(Rd) acting in the space L(R). If V = 0 then the operator has purely absolutely continuous spectrum on (0,+∞). We find conditions on V which guarantee that the absolutely continuous spectrum of both operators H+ = −∆ + V and H− = −∆− V is essentially supported by [0,∞). This means that the spectral projection associated to any sub...
متن کاملSome Estimates of Schrödinger-Type Operators with Certain Nonnegative Potentials
where the potential V belongs to Bq1 for q1 ≥ n/2. We are interested in the L boundedness of the operator∇4H−1, where the potential V satisfies weaker condition than that in 5, Theorem 1, 2 . The estimates of some other operators related to Schrödinger-type operators can be found in 2, 5 . Note that a nonnegative locally L integrable function V on R is said to belong to Bq 1 < q < ∞ if there ex...
متن کاملSome Schrödinger Operators with Dense Point Spectrum
Given any sequence {En}n−1 of positive energies and any monotone function g(r) on (0,∞) with g(0) = 1, lim r→∞ g(r) = ∞, we can find a potential V (x) on (−∞,∞) so that {En}n=1 are eigenvalues of − d 2 dx2 + V (x) and |V (x)| ≤ (|x| + 1)−1g(|x|). In [7], Naboko proved the following: Theorem 1. Let {κn}∞n=1 be a sequence of rationally independent positive reals. Let g(r) be a monotone function o...
متن کاملSome Quantum Operators with Discrete Spectrum but Classically Continuous Spectrum
A standard rule of thumb about whether a quantum Hamiltonian H = -A + V(x) has purely discrete spectrum or some continuous spectrum is the following. Look at the volume {(p, q) Ip* + V(q) <E} in R*“. If this volume is finite for all E, the standard wisdom is that H has only discrete spectrum. This standard wisdom also says that if this volume is infinite for some E < oo, then the spectrum is no...
متن کاملSchrödinger Operators with Singular Potentials †
We describe classical and recent results on the spectral theory of Schrödinger and Pauli operators with singular electric and magnetic potentials
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2006
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2006.01.006