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This tag is for questions relating to Hilbert Space, a vector space equipped with an inner product, an operation that allows defining lengths and angles, and the space is complete. It arises naturally and frequently in mathematics and physics, typically as infinite-dimensional function spaces having the property that it is complete. Applies also to pre-Hilbert spaces, rigged Hilbert spaces, and spaces with negative norm or zero-norm states.

1 vote
0 answers
114 views

Give me an example of a differential operator that is normal, not self-adjoint and has appli... [closed]

I am looking for an example of a differential operator whose domain is the Hilbert space of square integrable functions with real $N$-dimensional domain $L^2(\mathbb R^N)$ having the following charact …
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3 votes
2 answers
544 views

What is the precise definition of state of a quantum system?

On studying quantum states of the hydrogen atom, I came with a question: what is the precise definition of a quantum state? Particularly, when solving the Schroedinger eq for the H using separation of …
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