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ܼ

ư

\Psi~=~A~e^{i~\(~kx~-~\omega~t~\)}

ޤưؿt2ʬ롣

\frac{\partial^2~\Psi}{\partial~t^2}~=~-~\omega^2~\Psi

ޤưؿx2ʬ롣

\frac{\partial^2~\Psi}{\partial~x^2}~=~-~ka^2~\Psi

ξȤ⦷о줷ΤǡäȼΤ褦˷׻Ǥ롣

-~\frac{1}{\omega^2}\frac{\partial^2~\Psi}{\partial~t^2}~=\Psi=-~\frac{1}{k^2}\frac{\partial^2~\Psi}{\partial~x^2}

\frac{\partial^2~\Psi}{\partial~x^2}=\frac{k^2}{\omega^2}\frac{\partial^2~\Psi}{\partial~t^2}

ǡk=2/ˤꡢΩġ

k=\frac{2~\pi}{\lambda}=\frac{2~\pi~\nu}{\nu~\lambda}=\frac{\omega}{v}

\frac{k}{\omega}=\frac{1}{v}

äơưؿʬϼΤ褦ˤʤ롣

\frac{\partial^2~\Psi}{\partial~x^2}=\frac{1}{v^2}\frac{\partial^2~\Psi}{\partial~t^2}

ưǤ롣

ưؿñȤΤҤȤĤɽƤ˲᤮ʤưäƤ򤤤ơʤɤβФΤǤϲ򤫤ưƳ櫓Ǥ롣ºݤˡưβˤʤ뤳ȤåƤ館Ф狼롣

ư2

2ʿȤ(x,y,z)Ȥ롣xy줾ʬΤȤʤ롣ʤʤȤοʹ˿ľŬʿ̤2ȤڤäȤȡȤʱ߾ΤɤȤª롣ʱ߾εפ2ʿȦǤ롣

ǥ٥ȥrĹr=|r|)2Ȥΰ֤ɽ٥ȥȤ롣rϤʱCˤ롣

ȡޤ2ȤϼΤ褦ɽ롣

\Psi~=~A~\sin~\(kr~\cos~\theta~-~\omega~t\)

ưؿ\Psi~=~A~\sin~\(~kx~-~\omega~t\)xΤkrcosȤǤ롣ĹˤȤСk=/2ФǤ롣

ǥ٥ȥkͤ򤳤kˤԹ礬褤kʬ(kx,ky)ϼʤФʤʤ

k=~\sqrt{k_{x}^{2}+k_{y}^{2}}=\frac{\lambda}{2~\pi}

Υ٥ȥkȿ٥ȥť٥ȥȤ

٥ȥkrѤ\mathbf{k}~\cdot~\mathbf{r}~=kr~\cos~\thetaȤʤ뤫顢2ưؿϼΤ褦ˤʤ롣

\Psi~=~A~\sin~\(~\mathbf{k}~\cdot~\mathbf{r}~-~\omega~t~\)

ư3

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