Variational methods in relativistic quantum mechanics
نویسندگان
چکیده
منابع مشابه
Variational methods in relativistic quantum mechanics
This review is devoted to the study of stationary solutions of linear and nonlinear equations from relativistic quantum mechanics, involving the Dirac operator. The solutions are found as critical points of an energy functional. Contrary to the Laplacian appearing in the equations of nonrelativistic quantum mechanics, the Dirac operator has a negative continuous spectrum which is not bounded fr...
متن کاملVariational Methods in Relativistic Quantum Mechanics: New Approach to the Computation of Dirac Eigenvalues
1 Abstract. The main goal of this paper is to describe some new variational methods for the characterization and computation of the eigenvalues and the eigenstates of Dirac operators. Our methods are all based on exact variational principles, both of min-max and of minimization types. The minimization procedure that we introduce is done in a particular set of functions satisfying a nonlinear co...
متن کاملCanonical Relativistic Quantum Mechanics
Born proposed a unification of special relativity and quantum mechanics that placed position, time, energy and momentum on equal footing through a reciprocity principle and extended the usual position-time and energy-momentum line elements to this space by combining them through a new fundamental constant. Requiring also invariance of the symplectic metric yields as the invariance group, the in...
متن کاملRelativistic Non-Hermitian Quantum Mechanics
We develop relativistic wave equations in the framework of the new non-hermitian PT quantum mechanics. The familiar Hermitian Dirac equation emerges as an exact result of imposing the Dirac algebra, the criteria of PT -symmetric quantum mechanics, and relativistic invariance. However, relaxing the constraint that in particular the mass matrix be Hermitian also allows for models that have no cou...
متن کاملVariational Methods for Nonsmooth Mechanics
In this thesis we investigate nonsmooth classical and continuum mechanics and its discretizations by means of variational numerical and geometric methods. The theory of smooth Lagrangian mechanics is extended to a nonsmooth context appropriate for collisions and it is shown in what sense the system is symplectic and satisfies a Noether-style momentum conservation theorem. Next, we develop the f...
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: Bulletin of the American Mathematical Society
سال: 2008
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-08-01212-3