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Results tagged with hilbert-space
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user 295819
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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Diagonalizing a given Hamiltonian
The following Hamiltonian, which has to be diagonalized, is given:
$H = \epsilon(f^{\dagger}_1f_1 + f_2^{\dagger}f_2)+\lambda(f_1^{\dagger}f_2^{\dagger}+f_1f_2)$
$f_i^{\dagger}$ and $f_i$ represent …
- 59
4
votes
3
answers
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Confusion about ladder operators
Let´s consider a system, that consists out of $N$ bosonic particles, that are not interacting with each other. The Hamiltonian of this system would be given as
$$H = \sum_{i=1}^N \frac{\hbar^2}{2m}\ha …
- 59