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Results tagged with hilbert-space
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user 251538
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.
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Mathematical issue regarding a variant of Quantum Harmonic Oscillator
Suppose I have a potential of the form $$V(x) = \begin{cases} \frac{1}{2}kx^2 &\text{ if }x>0 \\ {\infty} &\text{ if }x<0 \end{cases} $$
We know for the usual HO one introduces $a$ and $a^{\dagger}$ …
- 395
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Do eigenfunctions of the position and momentum operators vary from one problem to another?
Now the eigenfunctions of the Hamiltonian clearly differ from one problem to another since the Hamiltonian depends on the potential and hence for a different potential we get a different eigenvalue eq …
- 395