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Completeness of Landau basis
We know that the Landau Hamiltonian (uniform magnetic field) is diagonalized by wavefunctions $|n,m\rangle,n,m\in \mathbb{N}$ in the symmetric gauge. However, does this set of functions form a "...
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Is mathematical rigour irrelevant in most physics fields? [duplicate]
Are mathematical notions like closed sets, limits of sequences, measures, and function spaces basically irrelevant in the day to day work of a physicist? Naturally, such concepts are the foundations ...
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Path dependent phase in quantum mechanics
In elementary treatments of quantum mechanics, we are taught that the wavefunction of a single particle is complex valued ($\Psi : \mathbb{R}^3 \to \mathbb{C}$). In particular, the wavefunction has a ...
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Why isn't the path integral defined for non-homotopic paths?
Context
In the Aharonov Bohm effect, there is a solenoid which creates a magnetic field. Since the electron cannot be inside the solenoid, the configuration space is not simply connected.
Question
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Doubts about the Aharonov-Bohm effect
In F. Schwabl, Quantum Mechanics p.148 it is explained that if we have a particle in an electromagnetic field given by potentials $\varphi$ and $\mathbf{A}$ with wave function $\psi$, then a gauge ...
