鍘熷瓙绲�(ji茅)妲�(g貌u)

1.鏍稿闆诲瓙鐨勯亱(y霉n)鍕�(d貌ng)鐗规€�

鏍稿闆诲瓙閬�(y霉n)鍕�(d貌ng)鍏锋湁鑳介噺閲忓瓙鍖栥€佹尝绮掍簩璞℃€у拰绲�(t菕ng)瑷�(j矛)鎬х殑鐗瑰緛锛屼笉鑳界敤缍�(j墨ng)鍏哥殑鐗涢爴鍔涘(xu茅)渚�(l谩i)鎻忚堪鏍稿闆诲瓙鐨勯亱(y霉n)鍕�(d貌ng)鐙€鎱�(t脿i)銆�

2.鏍稿闆诲瓙鐨勯亱(y霉n)鍕�(d貌ng)瑕�(gu墨)寰嬬殑鎻忚堪

鐢变簬寰绮掑瓙鍏锋湁娉㈢殑鐗规€э紝鎵€浠ュ湪閲忓瓙鍔涘(xu茅)涓敤娉㈠嚱鏁�(sh霉)Ψ渚�(l谩i)鎻忚堪鏍稿闆诲瓙鐨勯亱(y霉n)鍕�(d貌ng)鐙€鎱�(t脿i)锛屼互浠ｆ浛缍�(j墨ng)鍏稿姏瀛�(xu茅)涓殑鍘熷瓙杌岄亾姒傚康銆�

(1)娉㈠嚱鏁�(sh霉)Ψ(鍘熷瓙杌岄亾)锛氱敤绌洪枔鍧愭(bi膩o)渚�(l谩i)鎻忓娉㈢殑鏁�(sh霉)瀛�(xu茅)鍑芥暩(sh霉)寮�,浠ヨ〃寰佸師瀛愪腑闆诲瓙鐨勯亱(y霉n)鍕�(d貌ng)鐙€鎱�(t脿i)銆�

涓€鍊�(g猫)纰哄畾鐨勬尝鍑芥暩(sh霉)Ψ锛岀ū鐐轰竴鍊�(g猫)鍘熷瓙杌岄亾銆�

(2)姒傜巼瀵嗗害(骞剧巼瀵嗗害)锛�Ψ2琛ㄧず寰绮掑瓙鍦ㄧ┖闁撴煇浣嶇疆鍠綅楂旂⿳鍏�(n猫i)鍑虹従(xi脿n)鐨勬鐜囧嵆姒傜巼瀵嗗害銆�

(3)闆诲瓙浜戯細鐢ㄩ粦榛�(di菐n)鐤忓瘑鐨勭▼搴︽弿杩板師瀛愭牳澶栭浕瀛愬嚭鐝�(xi脿n)鐨勬鐜囧瘑搴�(Ψ2)鍒嗗竷瑕�(gu墨)寰嬬殑鍦栧舰銆傞粦榛�(di菐n)杓冨瘑鐨勫湴鏂�,琛ㄧず闆诲瓙鍑虹従(xi脿n)鐨勬鐜囧瘑搴﹁純澶�,鍠綅楂旂⿳鍏�(n猫i)闆诲瓙鍑虹従(xi脿n)鐨勬(j墨)鏈�(hu矛)杓冨銆�

(4)鍥涘€�(g猫)閲忓瓙鏁�(sh霉):娉㈠嚱鏁�(sh霉)Ψ鐢眓.l.m涓夊€�(g猫)閲忓瓙鏁�(sh霉)姹哄畾锛�

涓夊€�(g猫)閲忓瓙鏁�(sh霉)鍙栧€肩浉浜掑埗绱勶細

1) 涓婚噺瀛愭暩(sh霉)n鐨勭墿鐞嗘剰缇╋細

n鐨勫彇鍊硷細n=1,2,3锛�4……∞ ,

鎰忕京锛� 琛ㄧず鏍稿鐨勯浕瀛愬堡鏁�(sh霉)骞剁⒑瀹氶浕瀛愬埌鏍哥殑骞冲潎璺濋洟;纰哄畾鍠浕瀛愬師瀛愮殑闆诲瓙閬�(y霉n)鍕�(d貌ng)鐨勮兘閲忋€�

n = 1锛�2锛�3锛�4, ……∞锛� 灏�(du矛)鎳�(y墨ng)浜庨浕瀛愬堡K锛孡锛孧锛孨, ···

鍏锋湁鐩稿悓n鍊肩殑鍘熷瓙杌岄亾绋辩偤铏曚簬鍚屼竴闆诲瓙灞�銆�

2) 瑙掗噺瀛愭暩(sh霉)ι:

ι鐨勫彇鍊硷細鍙梟鐨勯檺鍒讹紝ι= 0,1,2……n-1 (n鍊�(g猫))銆�

鎰忕京锛氳〃绀轰簽灞�锛岀⒑瀹氬師瀛愯粚閬撶殑褰㈢媭;灏�(du矛)浜庡闆诲瓙鍘熷瓙锛岃垏n鍏卞悓纰哄畾鍘熷瓙杌岄亾鐨勮兘閲�銆�…

ι鐨勫彇鍊硷細 1 锛� 2 锛� 3 锛� 4

闆诲瓙浜炲堡锛� s, p, d, f……

杌岄亾褰㈢媭锛� 鐞冨舰 绱￠寴褰� 姊呰姳褰� 寰�(f霉)闆�

鍦�3-1

3) 纾侀噺瀛愭暩(sh霉)m:

m鐨勫彇鍊硷細鍙�ι鐨勯檺鍒�锛� m=0 ,±1,±2……±ι(2ι+1鍊�(g猫)) 銆�

鎰忕京锛氱⒑瀹氬師瀛愯粚閬撶殑绌洪枔鍙栧悜銆�

ι=0锛� m=0锛� s杌岄亾绌洪枔鍙栧悜?y脿n)?;

ι=1, m=0 ,±1锛� p杌岄亾绌洪枔鍙栧悜?y脿n)?;

ι=2, m=0 ,±1,±2 , d杌岄亾绌洪枔鍙栧悜?y脿n)?;

……

n锛�ι鐩稿悓鐨勮粚閬撶ū鐐虹瓑鍍�(ji脿)杌岄亾銆�

涓€鍊�(g猫)鍘熷瓙杌岄亾鏄寚n銆�ι銆乵涓夌ó閲忓瓙鏁�(sh霉)閮藉叿鏈変竴瀹氭暩(sh霉)鍊兼檪(sh铆)鐨勪竴鍊�(g猫)娉㈠嚱鏁�(sh霉)Ψ(n,ι,m)锛屼緥濡�Ψ(1,0,0)浠ｈ〃鍩烘厠(t脿i)姘師瀛愮殑娉㈠嚱鏁�(sh霉)銆�

n銆�ι銆乵鍙栧€煎悎鐞嗘墠鑳界⒑瀹氫竴鍊�(g猫)瀛樺湪鐨勬尝鍑芥暩(sh霉)锛屼害鍗崇⒑瀹氶浕瀛愰亱(y霉n)鍕�(d貌ng)鐨勪竴鍊�(g猫)杌岄亾銆�

n銆�ι銆乵鐨勫彇鍊艰垏娉㈠嚱鏁�(sh霉)锛�

n=1(1鍊�(g猫)), ι=0,m=0, Ψ(1,0,0)

n=2(4鍊�(g猫)), ι={

n=3(9鍊�(g猫)), ι={

n=4(16鍊�(g猫))

……

娉㈠嚱鏁�(sh霉)Ψ鏁�(sh霉)鐩�=n2

鍦ㄤ竴鍊�(g猫)纰哄畾鐨勫師瀛愯粚閬撲笅锛岄浕瀛愯嚜韬倓鏈夊叐绋笉鍚岀殑閬�(y霉n)鍕�(d貌ng)鐙€鎱�(t脿i)锛岄€欑敱mS纰哄畾.

鎰忕京锛氫唬琛ㄩ浕瀛愯嚜韬叐绋笉鍚岀殑閬�(y霉n)鍕�(d貌ng)鐙€鎱�(t脿i)(缈�(x铆)鎱ｄ互闋�銆侀€嗚嚜鏃嬪叐鍊�(g猫)鏂瑰悜褰㈠閫欏叐绋笉鍚岀殑閬�(y霉n)鍕�(d貌ng)鐙€鎱�(t脿i),鍙敤↑↑ 琛ㄧず鑷棆骞宠,↑↓琛ㄧず鑷棆鍙嶅钩琛�銆�

閫欐ǎn銆�ι銆乵銆乵S鍥涘€�(g猫)閲忓瓙鏁�(sh霉)纰哄畾闆诲瓙鐨勪竴鍊�(g猫)瀹屾暣鐨勯亱(y霉n)鍕�(d貌ng)鐙€鎱�(t脿i),浠�Ψ(n,ι,m, mS)琛ㄧず銆�

渚嬶細Ψ(1,0,0,+ ),Ψ(1,0,0,- ) 锛�Ψ(2,1,1,+ ) 锛�Ψ(2,1,1, - ) 绛夌瓑