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Results tagged with operators
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user 250811
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 $\times$, $+$!
10
votes
Commutator and Taylor series in quantum mechanics
This is simply an identity of Taylor expansion and has nothing to do with the fact that you have operators around, if
$$f(x)=\sum_n \frac{f^{(n)}(0)}{n!} … The reason for that is that analytic functions of operators are defined by their Taylor series. …
- 465
0
votes
Using Schwarz's Inequality to show an expectation value relationship of a particle
For the Cauchy-Schwartz inequality you need to have some inner product that you can use. The inner product you used
$$\left\langle f,g\right\rangle=\int f(x)g(x)dx$$
is valid, but the definition
$$\le …
- 465
0
votes
Accepted
Examples of the physical significance and importance of matrix diagonalization and eigenvalu...
This is not a physics application per se, but I remember that as a first year undergrad I was convinced in the usefulness of matrix diagonalization by the application to obtain a closed expression for …
- 465
1
vote
How should I solve the Schrödinger equation by diagonalization in QFT?
Assuming that I understand the question correctly, the answer is not specifically about the AIM, but in general about second-quantized operators. … The crucial thing to understand is that the ladder operators $c_{k\sigma}$ do not act on the Hilbert space $L^2(\mathbb{R}^n)$, but rather on the Fock space, whose basis is given by the occupation numbers …
- 465