Answer by Simon for What are the adequate Hilbert spaces for Schrödinger,...
Here is another approach. Instead of defining a state space $L^2(\text{something})$ and then defining observables as the self-adjoint operators on that space, you can go the other way around:Choose an...
View ArticleAnswer by ZeroTheHero for What are the adequate Hilbert spaces for...
One way to proceed is to start with the classical observable and find some suitable Lie algebra containing these as generators. Upon quantization, the observables are promoted to operators, now acting...
View ArticleAnswer by ACuriousMind for What are the adequate Hilbert spaces for...
Ordinary QM has essentially a fixed Hilbert space of $L^2(\mathbb{R}^n)\otimes S$, where $n$ is the number of spatial dimensions and $S$ some representation of the rotation group. This is due to the...
View ArticleWhat are the adequate Hilbert spaces for Schrödinger, Schrödinger–Pauli,...
In quantum mechanics (both non-relativistic and relativistic), it is possible to study physical systems by looking for solutions of PDEs, whose solutions belong to suitable Hilbert spaces:Schrödinger...
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