【数学物理方法课件】δ函数（可编辑）

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1、δ
4δ
4Green2
δ1δδδP.A.M.Dirac!"#$%&'*+,-./#01234152617869:;?@Aδ+,BCDEFGHI4GJKLMKNOPQVWXY-RSJKTUZ[LZ]+,^_`a$bcdefghHδijlmnopqrstu*δkSvwxyz'K

2、rs*z~

3、δ~

4、§10.1δ2§10.1δ??C^;34^δ?1617878K?x??10.1￠￡?￠¤￥

5、§10.1¨?a-?0xlˉ°±23′μ????1o1?ˉ°àa???á????l?;?0,?x???2δx?1,??lxl;l?l22??l??0,?x2.?èéê??D?òó2??l/2xl/2±ìíμfx∞fxδxdxfθl,?1/2≤θ≤1/2.l?∞×òù±∞ú?a?l/2,bl/2ü2abfxδxdxfθl,?1/2≤θ≤1/2.Yüa??T×?à?l→0á???μ???0,?x0;?δ

6、xlimδx?∞,?x0;ll→0???0,?x0.?èéê????x0ìíμfx2∞fxδxdxf0.?∞×òù±∞ú?a0,b0ü2abfxδxdxf0.èéê+,?ìí?78K??e^òó?÷?Aù?*C^`gú_`?üXYyFZ[
δ3tê
t?δ?ù?μ2?°μμ?δx0,?x0;∞,?x0?ê
ê
?ù2μéêú?ùμùDδμμT×ê
2∞fxδxdxf0,ù∞δxdx1.?∞?∞?ó!???∞fxδxdxlim∞fxδxdx.ll→0

7、?∞?∞"#'?è+,?#?./μ$?%&δμμ*-6T2è23;?#;×μ01ù2456μìí78μ9:μDδ?Yéê
?ètó?;ò??ìíμδμ@?δxx0ìí2ìí@?μéêfx2∞∞∞fxδxdxfxδx?fxδxdx?∞?∞?∞?f0.üYB??C-?Aδμìí?D?tùB???EtB?C3?Iòδ?μ?°μ?FG2H6μJKLù32lim∞fxδxdxf0ll→0?∞378μδxù2llim∞fxδnxdxf0n→∞?∞Mù78μδnxμT×Nδ§10.1δ4n22n1si

8、nnx?nxe√ππ1+n2x2πx?10.2δOP￡QRSTUVKE"ê
XY

9、2δμW?ó!xδx0,δ?xδx,δ?x?δx,1δaxδx,

10、a

11、gxδxg0δxü?ó!?∞fxxδxdx0,?∞∞fxδ?xdx∞fxδxdx,?∞?∞∞∞fxδ?xdx?fxδxdx,?∞?∞∞fxδaxdx∞fx1δxdx,?∞?∞

12、a

13、∞∞fxgxδxdxfxg0δxdx.?∞?∞δZ;:[Wμ2èxδxdxηx,?∞]^dηxδx.dx
δ5?Y_E;δLaplaceδt?t∞δt?te?ptdte?pt0,t0.0000δE;:[W

14、μFourier]?∞δxe?ikxdx1,?∞;Fourier_μ`abK2δx1∞eikxdk.2π?∞cdefdδgh?ij?x,y???üùδx?xδy?y002???Gkμ100?lmn??üù°x,y,z2???μ1δx?xδy?yδz?00000z0"?lmnom?ùlmnjqm?üùlmn°%&???°±μ???p???°±-μ???r10.1st1?2?4πδr,ruD?2?2?2?2≡++?x2?y2?z2v222?Laplacewrx+y+z,δrδxδyδzxyjù

15、K"?ê
Xó!*XFzμLδμWN?

16、st?21dxdydz0,?r0∈V;r?4π,?r0∈V.V?r0á?~a?1x?xx2+y2+z2?x2+y2+z23/2,?213x2?x2+y2+z2.?x2x2+y2+z2x2+y2+z25/2ó?213y2?x2+y2+z2?y2x2+y2+z2x2+y2+z25/2,?213z2?x2+y2+z2.?z2x2+y2+z2x2+y2+z25/2§10.1δ6lK*a1?20,r0.rCüa????s?V±r0á0???2è???j?V±r0á1/rr0?@μ:?ü/lmn°a?áV?21dxdydzli