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Results tagged with operators
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user 219318
In physics, an operator is almost always either a square matrix or a linear mapping between two function spaces (defined on, say, $\mathbb R^n$). Operators serve as observables and as time evolution operators in Quantum Mechanics. This tag will most often find valid use in quantum mechanics; don't use this tag just because your equations contain "everyday operations" like $\times$, $+$!
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Why energy eigenstates form orthonormal basis
The first important property of a Hermitian operator is that it only has real eigenvalues. Try show it yourself starting from the eigenvalue equation:
$$ \hat H \psi_n(x) = E_n\psi_n(x)$$
taking adjoi …
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Three operators commuting with each other
The proof can be constructed based on the proof for just 2 operators (for example, see here), with essentially the same steps for the nondegenerate case. …
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Different definitions of commutator in operator theory/quantum mechanics vs. in group theory
In group theory, the commutator of two elements $g$ and $h$ in a group is defined as $$[g,h]=ghg^{-1}h^{-1}$$
However, in quantum mechanics, we always see commutator relation between two operators $A$ … I understand that operators in QM are in the Hilbert space, which has an additional vector space structure besides the group structure. …
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Examples of antiunitary operator other than time reversal operator
I wonder what are some other examples of anti-unitary operators that appear in the context of quantum mechanics, or physics in general. …
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Examples of antiunitary operator other than time reversal operator
Just for future reference, an example I encountered recently is the following: in the Bogoliubov-de Gennes (BdG) theory of superconductivity, the Hamiltonian has particle-hole symmetry. And the corres …
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