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Linear Operators for Quantum Mechanics Thomas F. Jordan
Publisher: Dover Publications

Though quantum mechanics is formally a theory of vector spaces and linear transformations, Heisenberg did not even know what a linear operator or matrix was when he began the theory! The Choi-Jamiołkowski isomorphism is an isomorphism between linear maps from Hilbert space \({\cal H}\) to Hilbert space \({\cal K}\) and operators living in the tensor product space \({\cal H}\otimes{\cal K}\). (The following are my Namely, we can write the wave function as a linear combination of its eigenfunctions. Quantum Mechanics: General Structure of Wave Mechanics and Operator Methods. Ježek, Maximum-likelihood methods in quantum mechanics, In M. Then, the special case of a nominal linear quantum system is considered with non-linear perturbations to the system coupling operator. Anti-linear transformations appear in quantum mechanics exclusively for time-reversal transformations. Operators in quantum mechanics, Linear & Abstract Algebra, 4. Řeháček, Eds., Quantum State Estimation, Lecture Notes in Physics, Springer 2004. Special types of linear operators (Hermitian, unitary, inverse) and their properties. The book is not aimed at experts in constructive or field theory and the algebra of local observables. Quantum Mechanics : Operators in Advanced Physics Homework is being discussed at Physics Forums. The book does not assume the reader is an expert in operator algebra, though some familiarity with quantum mechanics, quantum field theory and special relativity is a prerequisite. Topics here include: operator algebras (von Neumann, c* and w*), factors, positive linear forms and states, the GNS construction, nets of algebras of local observables and vacuum states. First, the abstract definition: if T, L: V → V are linear operators on a vector space V over a field K, then L is said to be a ladder operator for T if there is a scalar c ∈ K such that the commutator of T and L satisfies. These are some notes, mostly for my own benefit, on annihilation, creation, and ladder operators in quantum mechanics, with a few remarks towards the end on angular momentum, spin and Clebsch–Gordan coefficients. \displaystyle [T, L] := TL - LT = cL. Let us denote {\widehat{R}|\psi(\mathbf{z}) with {\widehat{R}} the operator of an elementary time-reversal transformation.