Amath105-8.pdf - IV Infinite series Talyor series Convergence and its region Applied to Physical Chemistry II Fourier series Particle in one-dimensional

Amath105-8.pdf - IV Infinite series Talyor series...

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IV. Infinite series IV. Infinite series • Talyor series • Convergence and its region • Applied to Physical Chemistry II • Fourier series • Particle in one-dimensional box (PC II) • Kronecker delta function • Fourier transforms
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L x L ( ) L x in n n e c x f / π −∞ = = ( ) = L L L x in n dx e x f L c / 2 1 π ( ) L x in n e L x / 2 1 π φ = Define ( ) ( ) mn n L L m dx x x δ φ φ = * L , 2 , 1 , 0 , ± ± = m n delta function ( ) ( ) x c x f n n n φ −∞ = = ( ) ( ) = L L n n dx x x f c φ Fourier series
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