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.

928 questions
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Confusion regarding $|A|^2 \int\limits_{-\infty}^\infty e^{i(p-p')x/h}=|A|^2 2\pi h\delta(p-p')$

The book "Introduction to Quantum Mechanics (Second edition)" by Griffiths says the following on pg 103: $$|A|^2 \int\limits_{-\infty}^\infty e^{i(p-p')x/h}=|A|^2 2\pi h\delta(p-p')$$ Here $\delta$...
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Lifting representation Heisenberg algebra

I (think) I've found the Heisenberg Lie algebra representation through quantization. Where we have $q \mapsto q$ and $p \mapsto -i \hbar \frac{\partial}{\partial q}$. So this is only a Lie algebra ...
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Coarsenings In Deutsch Et Al's Constructor Theory

Disclaimer: I posted a questions on constructor theory here a few days ago but received two closing votes, I guess because it consisted of several subquestions, so I deleted it and now try to focus on ...
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Hamiltonian Flows and Heisenberg picture of quantum mechanics

I am a math bachelor student studying Quantum Mechanics and I was very briefly introduced to the Heisenberg picture. (Hence many of the following may be trivial) In particular what I know is that: ...
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What are the automorphisms on the strucuture consisting of the nonzero vectors of a Hilbert space with the orthogonality relation?

Let $V$ be an infinite-dimensional complex Hilbert space. With this space we can associate a relational structure $V^+ = (V^+, \bot)$, where $V^+$ is the set of non-zero vectors in $V$, and $\bot$ ...
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When is $\exp(-iHt)$ well-defined?

If $H$ is a linear operator, what restrictions should be put on $H$ in order for $\exp(-iHt)$ to be well defined? How do you define $\exp(-iHt)$ when $H$ is infinite-dimensional? (If it is possible)
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Mathematically rigorous Quantum Mechanics

I am a student of mathematics attending a course in Quantum Mechanics. This course is held by a physicist, and it is really confusing for me to follow his reasonments. With this, I do not mean to be ...
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Is there a construction of the Wiener measure by discretization and limits which parallels the Physics ideas?

In Physics one constructs the path integral by a limiting process together with a discretization procedure. Now, in order to better paralell with the Wiener measure, consider this in Euclidean ...
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Showing that any linear operator can be written as a sum of Hermitian matrices [duplicate]

Let $(V, \mathbb{C})$ be a complex - valued vector space. Let $A$ be any linear operator acting on this vector space. Suppose that $B = \{|v\rangle_{k}\}_{k=1}^{n}$ is a basis set for $(V, \mathbb{C})$...
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Technical operator theory question on Albeverio's “Solvable Models in quantum mechanics”

I'm currently studying S. Albeverio's book "Solvable models in quantum mechanics" where some technical things are used that I don't fully understand. It is a general technical operator theory question,...
Preparing for a presentation at university (I'm a Bachelor physics student) I have come across the formula below containg the time-ordering operator $T$. Although i have now understood the action of ...