Quantum Mechanical Operators

Bai Yin-bu

The concept of a linear operator in quantum mechanics was studied.Through the establishment of operator function's differential calculus,the concept of super-operator was introduced,and all kinds of the super-operator were given the definition,typical problems in quantum mechanics were analyzed on the base of the super-operator's use.The results show that the super-operator concept in quantum mechanics has wide applications and make physical meaning more clear.

George H. Duffey

Victor M. Galitski, Boris Mikhailovich Karnakov, Vladimir I Kogan +1 more

Abstract Mathematical formalism of quantum mechanics is closely connected with the theory of linear operators. A key quantum-mechanical principle is that physical quantities (observables) are represented by Hermitian linear operators that act on state vectors that belong to a Hilbert vector space. This chapter analyzes problems that deal with the basic concepts of the theory of linear operators; eigenfunctions, eigenvalues, mean values; the projection operators; quantum-mechanical representations of operators and wave-functions; and unitary operators.

Peter Joshua Atkins, Ronald Friedman

Operators in quantum mechanics Linear operators Eigenfunctions and eigenvalues Representations Commutation and non-commutation The construction of operators Integrals over operators Dirac bracket and matrix notation Hermitian operators The postulates of quantum mechanics States and wavefunctions

Ken F. Riley