Eigen-Wavefunction of infinite square well is $$\psi(x)=\sqrt{2/l}\sin(n\pi x/l).$$ I want to write Husimi $Q$ function for infinite square well. General expression of Q function is $$Q=(1/2)\pi \langle \alpha|\rho|\alpha\rangle.$$ But I can’t use it for infinite square well as coherent states are written in term of superposition of eigenstates of harmonic oscillator. Also I don't want to solve Wigner function of infinite square well first and then find Q-function. I need to find Q-function directly. How could we find Q-function generally?
$\begingroup$
$\endgroup$
3
-
$\begingroup$ Are you comfortable with $ \langle x | \alpha\rangle= {e^{-\frac{(x-\sqrt{2}\Re(\alpha))^2}{2} +ix \sqrt{2} \Im (\alpha)}} / {\pi^{1/4}} $ ? $\endgroup$– Cosmas ZachosCommented Oct 1, 2022 at 19:43
-
$\begingroup$ @CosmasZachos: if you would have decided to use \exp instead of e^, then perhaps I would have been able to read what you wrote. :-) Perhaps next time? $\endgroup$– flippiefanusCommented Oct 2, 2022 at 3:42
-
$\begingroup$ $\langle x | \alpha\rangle= \exp ({-\frac{(x-\sqrt{2}\Re(\alpha))^2}{2} +ix \sqrt{2} \Im (\alpha)} ) ~/ {\pi^{1/4}} $ . $\endgroup$– Cosmas ZachosCommented Oct 2, 2022 at 10:48
Add a comment
|