# Tagged Questions

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.

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### Why do odd dimensions and even dimensions behave differently?

It is well known that odd and even dimensions work differently. Waves propagation in odd dimensions is unlike propagation in even dimensions. A parity operator is a rotation in even dimensions, ...
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### Mathematics needed in the study of Quantum Physics

As a 12th grade student , I'm currently acquainted with single variable calculus, algebra, and geometry, obviously on a high school level. I tried taking a Quantum Physics course on coursera.com, but ...
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### Correct spaces for quantum mechanics

The general formulation of quantum mechanics is done by describing quantum mechanical states by vectors $|\psi_t(x)\rangle$ in some Hilbert space $\mathcal{H}$ and describes their time evolution by ...
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### Topological Quantum Field theories

I was wondering about the following on TQFTs. It is said that TQFTs have vanishing Hamiltonians $\hat{\mathcal{H}}$. Firstly, I would like to ask: Why is this so? Secondly, consider the ...
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### Does this notion of morphism of noncommutative rings appear in the ring theory literature?

Definition: Let $R, S$ be two rings. A classical morphism $\phi : R \to S$ is a function from elements of $R$ to elements of $S$ which restricts to a homomorphism (of rings, in the usual sense) on ...
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### Takhtajan's “Quantum Mechanics for Mathematicians”

I want to know the math that is required to read Takhtajan's "Quantum Mechanics for Mathematicians". From the book preview on Google, I gather that algebra, topology, (differential) geometry and ...
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### Quantization of angular momentum: is Dirac's proof wrong?

I'm trying to understand the physicist's proof of the theorem on the spectral structure of angular momentum operators (I'm being told that this proof is due to Dirac). I will refer to Ballentine's ...
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### Does the shift operator on $\ell^2(\mathbb{Z})$ have a logarithm?

Consider the Hilbert space $\ell^2(\mathbb{Z})$, i.e., the space of all sequences $\ldots,a_{-2},a_{-1},a_0,a_1,a_2,\ldots$ of complex numbers such that $\sum_n |a_n|^2 < \infty$ with the usual ...
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### Physical (Quantum Mechanical) Significance of completeness of Hilbert Spaces.

I'm not sure if the question is very 'mathematical',but I'm asking any way. I have a basic knowledge of quantum mechanics and I'm studying Hilbert spaces. I was wondering what is the physical ...
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### Derivation of Schrödinger's equation

I recall a famous quote of the late physicist Richard Feynman: Where did we get that from? It's not possible to derive it from anything you know. It came out of the mind of SchrÃ¶dinger. This ...
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### “Fun” question: anyone know why $e$ (Euler's Number) was chosen for wave functions?

First, let me say that this is merely something I have always wondered about, and can never seem to find a good reference for. I simply want to know... the geek in me. Why was $e$ (Euler's Number) ...
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### Quantum Mathematics?

As per my last question, this has less to do with cold, hard, and fast calculations and more to do with the interplay between mathematics and philosophy...but as armchair philosophers aren't as hard ...
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### Applications of Operator Algebras to modern physics

I think that recently I've started to lean in my interest more towards operator algebras and away from differential geometry, the latter having many applications to physics. But while taking physics ...
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### Relationship between dual space and adjoint of a linear operator

I am having a hard time understanding the concept of adjoint of a linear operator. Given a finite dimensional Hilbert space $H$ over a field $F$, I know the dual space is the vector space $H^*$ of all ...
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