Linear Operators for Quantum Mechanics by Thomas F. Jordan

Linear Operators for Quantum Mechanics Thomas F. Jordan ebook
ISBN: 9780486453293
Publisher: Dover Publications
Format: pdf
Page: 160

If U is an isometry and ψ is a quantum state, then U ψ is again a quantum state. (Note that since the inner product is uniquely determined by a composition of linear functions and the norm, it follows that a linear operator between Hilbert spaces preserves the inner product if and only if it preserves the norm. Hilbert spaces are also fundamental to quantum mechanics, as vectors in Hilbert spaces (up to phase) describe (pure) states of quantum systems. ˆ� U ψ = ∫ ψ int U psi = int psi. Řeháček, Eds., Quantum State Estimation, Lecture Notes in Physics, Springer 2004. Ježek, Maximum-likelihood methods in quantum mechanics, In M. €� In stochastic mechanics, a stochastic operator is a linear map U : L 1 ( X ) → L 1 ( X ) such that. The spectral theory of linear operators plays a key role in the mathematical formulation of quantum 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}). You'll need to know a bit of math: calculus, a tiny bit probability theory, and linear operators on vector spaces. Today we'll develop and discuss some of the . You don't need to know quantum theory, though you'll have more fun if you do.