-1
votes
0answers
37 views

Wigner function for position eigenstates

What is the Wigner function (or $P$ or $Q$ function) associated with $|x\rangle\langle x|$? Thanks for any suggestion.
1
vote
0answers
20 views

Dipole Moment of Collection of Harmonic Oscillators [closed]

I am given the Hamiltonian of a collection of SHO with resonant frequencies $\omega_{n1}$ $$H = \sum_n\hbar\omega_{n1}[a_n^\dagger a_n+\frac12+\alpha_nE_0\cos(\omega t)(a_n+a_n^\dagger)]$$ Where ...
1
vote
1answer
242 views

Derivation for 7.14 in Atomic Physics by Foot

I was going thru Ch7 of Foot and trying to fill in the gaps. However I got stuck on (7.14). So Foot was working with a two level system with a small perturbation in the Hamiltonian resulted from an ...
-1
votes
1answer
206 views

Eigenvalue of Optical waveguide [closed]

Consider you have a slab waveguide having n1=3.5 and n2=1.45. The value of critical angel is 24.5 degree approx. Similarly effective refractive index will be in between 1.45 and 3.5. How can we find ...
6
votes
3answers
332 views

Commutator with a square root

How to find the commutator $[a, \sqrt{a^\dagger a}]$? Here $a$ is a usual bosonic annihilation operator, and $[a, a^\dagger] = 1$. The first thing I tried is $$ [x,A] = [x, \sqrt{A}]\sqrt{A} + ...
2
votes
1answer
140 views

Physical significance of effective wave function

In Yanhua Shih's book on quantum optics, the coherence functions are expressed in terms of effective wave function. Here are the expressions for single photon wave packets. To derive the coherence ...