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How to interpret the infinity of Hilbert Space?
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[QUOTE="Archeon, post: 5721249, member: 618958"] This is basically just a comprehension question, but what makes elements of the Hilbert space exist in infinite dimensions? I understand that the number of base vectors to write out an element, like a wavefunction, are infinite: \begin{equation*} \psi(x) = \int c_s u_s (x) ds = \sum_k^{\infty} \hat{c}_k \hat{u}_k(x) \end{equation*} So what are the bases u(x)? Are they just other wavefunctions that build a new wavefunction via superposition? And if so, how does this justify the infinite dimensions of the Hilbert space and why exactly is an infinite number of sub-wavefunctions necessary? Also apologies if I posted this in the wrong subforum, not really sure what this question classifies as. Thanks in advance. [/QUOTE]
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How to interpret the infinity of Hilbert Space?
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