Second order concentration near the binding energy of the helium schrodinger operator

1968 ◽  
Vol 6 (4) ◽  
pp. 311-337 ◽  
Author(s):  
P. A. Rejto
Keyword(s):  
Binding Energy ◽  
Schrödinger Operator ◽  
Second Order ◽  
Schrodinger Operator

scholarly journals On the Domains of Bessel Operators

2021 ◽  
Author(s):  
Jan Dereziński ◽  
Vladimir Georgescu
Keyword(s):  
Sobolev Space ◽  
Schrödinger Operator ◽  
Second Order ◽  
The Other ◽  
Bessel Operator ◽  
Bilinear Forms ◽  
Minimal Realization ◽  
Schrodinger Operator ◽  
Bessel Operators ◽  
Other Hand

AbstractWe consider the Schrödinger operator on the halfline with the potential $$(m^2-\frac{1}{4})\frac{1}{x^2}$$ ( m 2 - 1 4 ) 1 x 2 , often called the Bessel operator. We assume that m is complex. We study the domains of various closed homogeneous realizations of the Bessel operator. In particular, we prove that the domain of its minimal realization for $$|\mathrm{Re}(m)|<1$$ | Re ( m ) | < 1 and of its unique closed realization for $$\mathrm{Re}(m)>1$$ Re ( m ) > 1 coincide with the minimal second-order Sobolev space. On the other hand, if $$\mathrm{Re}(m)=1$$ Re ( m ) = 1 the minimal second-order Sobolev space is a subspace of infinite codimension of the domain of the unique closed Bessel operator. The properties of Bessel operators are compared with the properties of the corresponding bilinear forms.

scholarly journals Regularity for the second order Riesz transforms associated with Schrödinger operators on weighted BMO type spaces

2018 ◽  
Vol 20 ◽  
pp. 02005
Author(s):  
Trong Nguyen Ngoc ◽  
Dao Nguyen Anh ◽  
L. X. Truong
Keyword(s):  
Schrödinger Operator ◽  
Schrödinger Operators ◽  
Hölder’S Inequality ◽  
Second Order ◽  
Riesz Transforms ◽  
Schrodinger Operators ◽  
Schrodinger Operator ◽  
Weighted Bmo ◽  
Type Spaces ◽  
Weighted Case

Let L = −Δ + V be a Schrödinger operator on ℝn, where V is a nonnegative potential satisfying the suitable reverse Hölder’s inequality. In this paper, we study the boundedness of the second order Riesz transforms such as L−1∇2 on the spaces of BMO type for weighted case. We generalized the known results to the weighted case.

scholarly journals Applications of maximum modulus method and Phragmén–Lindelöf method for second-order boundary value problems with respect to the Schrödinger operator

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Zhen Liu
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Schrödinger Operator ◽  
Boundary Value ◽  
Maximum Modulus ◽  
Second Order ◽  
Schrodinger Operator ◽  
Uniqueness Of The Solution ◽  
Modulus Method

Abstract In this paper, we present a reliable combination of the maximum modulus method with respect to the Schrödinger operator (Meng in J. Syst. Sci. Complex. 16:446–452, 2003) and Phragmén–Lindelöf method (Shehu in Matematiche 64:57–66, 2015) to investigate the solution of a second-order boundary value problem with respect to the Schrödinger operator. We establish the uniqueness of the solution for this problem. The results reveal that this method is effective and simple.

scholarly journals On the two-dimensional Schrödinger operator with an attractive potential of the Bessel-Macdonald type

2020 ◽  
pp. 168385
Author(s):  
Wellisson B. De Lima ◽  
Oswaldo M. Del Cima ◽  
Daniel H.T. Franco ◽  
Bruno C. Neves
Keyword(s):  
Schrödinger Operator ◽  
Attractive Potential ◽  
Two Dimensional ◽  
Schrodinger Operator
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