bowerick.bsky.social
@bowerick.bsky.social
Reposted by bowerick.bsky.social
(Namely, for any ψ(x) in Hilbert space and any function φ(x), take the integral of φψ over x.)
So we have Φ as a subset of Η as a subset of Φ* -- the "Gelfand triple."
Things that we want to think of as eigenstates of x and p are actually elements of Φ*, of which H is a subset.
So we have Φ as a subset of Η as a subset of Φ* -- the "Gelfand triple."
Things that we want to think of as eigenstates of x and p are actually elements of Φ*, of which H is a subset.
October 15, 2025 at 2:31 PM
(Namely, for any ψ(x) in Hilbert space and any function φ(x), take the integral of φψ over x.)
So we have Φ as a subset of Η as a subset of Φ* -- the "Gelfand triple."
Things that we want to think of as eigenstates of x and p are actually elements of Φ*, of which H is a subset.
So we have Φ as a subset of Η as a subset of Φ* -- the "Gelfand triple."
Things that we want to think of as eigenstates of x and p are actually elements of Φ*, of which H is a subset.
Reposted by bowerick.bsky.social
Today in #QM1 we tackled those pesky unbounded operators like position and momentum. First we noted that in infinite dimensions "Hermitian" is not the same as "self-adjoint"; the latter requires identity of the domains of the operators and their adjoints. Important for proving various theorems.
October 15, 2025 at 2:24 PM
Today in #QM1 we tackled those pesky unbounded operators like position and momentum. First we noted that in infinite dimensions "Hermitian" is not the same as "self-adjoint"; the latter requires identity of the domains of the operators and their adjoints. Important for proving various theorems.