Questions tagged [quantum-mechanics]

For questions on quantum mechanics, a branch of physics dealing with physical phenomena at microscopic scales, where the action is on the order of the Planck constant.

929 questions
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Question about $e^{\frac{-itA}{\hbar}}(\hat{Q}+ \hat{P})e^{\frac{itA}{\hbar}}$

This arises in the context of trying to rigorously understand quantum dynamics but it's a functional analysis issue. For simplicity suppose we are in dimension $1$. Let $\hat{Q}$ be the operator ...
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Is the Unitary Group of a Hilbert Space a Lie group?

Let $H$ be an infinite-dimensional complex Hilbert space. Then the set of unitary operators on $H$ forms a group, known as the unitary group or Hilbert group. My question is, is this group a Lie ...
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Reference request for operator theory in Quantum mechanics

I am studying Shankar's Principles of Quantum Mechanics. In the first chapter where the author introduces the necessary mathematics tool for QM, the concept of derivatives of operators with respect to ...
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Dual pairing and inner product in a Hilbert space (and in $L^2(V)$)

I put beforehand that there are some similar questions in this blog, but I nonetheless would like to pose my question as I did not find any explanatory answer. Let us consider a vector space H, ...
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Computing the product $(\frac{d}{dx}+x)^n(-\frac{d}{dx}+x)^n$

I want to compute the product $$(\frac{d}{dx}+x)^n(-\frac{d}{dx}+x)^n,$$ for a natural number $n$. For $n$ equal to 0 or 1, the computation is very simple obviously, but for such a low number as 2 ...
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Hilbert space inequality in series expansion coefficients

In the context of some quantum-mechanical problem, there occurs a series development which gives the dependence of an "energy-type" eigenvalue $\varepsilon$ on some parameter $Q$. $\Psi_i$ are ...
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CNOT quantum gate using tensor products

In textbook, it states that the CNOT gate with the X gate applied on second qubit is \begin{array}{cccc} 1&0&0&0\\ 0&1&0&0\\ 0&0&0&1\\ 0&0&1&...