Linear Operators for Quantum Mechanics. Thomas F. Jordan

Linear Operators for Quantum Mechanics


Linear.Operators.for.Quantum.Mechanics.pdf
ISBN: 9780486453293 | 160 pages | 4 Mb


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



\displaystyle [T, L] := TL - LT = cL. As he says it further: “These assumptions are reasonable on account of the eigenvalues of real linear operators being always real numbers”. I'm sick and tired of heavy chunks of steel falling on my face. A representation of $\mathfrak h$ on a Hilbert space $X$ is a lie algebra homomorphism from $\mathfrak h$ to the set of linear operators on $X$ (with the commutator bracket). 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. Each observable state is represented by a maximally Hermitian (self-adjoint) linear operator. Of course, this problem today appears far from being settled and is a heavy burden left us by . 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. This question is hotly debated by people working in quantum optics, quantum computation and wherever foundations of quantum mechanics may enter. Will this happen to me as a quantum mechanic?





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