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Introductory Physics Homework Help
Solving Fourier Transform of T(t) to Find b(w) and Plot |b(w)|^2
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[QUOTE="v_pino, post: 3729694, member: 96104"] [h2]Homework Statement [/h2] An atom raised at t=0 to an excited state with energy [itex] E_0= \hbar \omega_0 [itex] has the time dependence [itex] T(t)=\frac{1}{\sqrt \tau}e^{-t/ 2 \tau} [itex] for t>0 and T(t)=0 for t<0. Thus the probability of being in an excited state decays exponentially with time. [itex] T(t)^2= \ frac {1} {\tau} e^ {-t/ \tau} [itex] a.) Find the transform b(w) of T(t). ('w' is omega, frequency) b.) Plot |b(w)|^2 as a function of w. c.) show that b(w) traces a circle on the complex plane as w runs from well below w_0 to well above it. [h2]Homework Equations[/h2] [tex] b(\omega)=\frac{1}{\sqrt{2 \pi}}\int{T(t)e^{i \omega t}} [/tex] The integral runs from -infinity to infinity. [h2]The Attempt at a Solution[/h2] [tex] b(\omega)=-\frac{1}{\sqrt{2 \pi \tau}}\frac{1}{i(\omega - \omega _0)-\frac{1}{2 \tau}} [/tex] When I do plot for part b, I get exponential incerase. Does that sound right? But when I do part (c), I don't get a circle nor elipse. [/QUOTE]
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Introductory Physics Homework Help
Solving Fourier Transform of T(t) to Find b(w) and Plot |b(w)|^2
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