設(shè)He原子的兩個核外電子的軌道分別是

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He原子的基態(tài)能級為

其中a0是半徑，讓a0由0.2增加到2.2步長是0.01，看看a0的變化對E有什么影響

得到的數(shù)據(jù)畫成圖

當(dāng)a0=1.19時，E取最小值，E=-2.8476

當(dāng)a0<0.59時，E為正，a0越小E越大

僅當(dāng)a0=1時，動能/勢能=-0.5，此時E=-2.75

隨著a0的增加，動能和相互作用能都在減小，勢能增加

He原子的基態(tài)能級為-2.90，這個方法得到的計算數(shù)值是實驗值的98.19%。

對比前述用類氫軌道得到的-2.75（94.8%）計算精度提高了3.37%。

import csvimport sympy import math from sympy import symbols, cancel, Lia = sympy.Symbol('a') e = sympy.Symbol('e') m = sympy.Symbol('m') h = sympy.Symbol('h') l = sympy.Symbol('l') lp = sympy.Symbol('lp') r = sympy.Symbol('r') EE = sympy.Symbol('EE') r1 = sympy.Symbol('r1') r2 = sympy.Symbol('r2') r3 = sympy.Symbol('r3')a0 = sympy.Symbol('a0')x = sympy.Symbol('x') y = sympy.Symbol('y') z = sympy.Symbol('z')θ1= sympy.Symbol('θ1') θ2= sympy.Symbol('θ2') Φ1= sympy.Symbol('Φ1') Φ2= sympy.Symbol('Φ2')θ= sympy.Symbol('θ') Ψ= sympy.Symbol('Ψ') Φ= sympy.Symbol('Φ') pi=sympy.Symbol('pi') E=sympy.Symbol('E') I=sympy.Symbol('I') sin=sympy.Symbol('sin') cos=sympy.Symbol('cos') diff=sympy.Symbol('diff') integrate=sympy.Symbol('integrate')pi=sympy.pi E=sympy.E sin=sympy.sin cos=sympy.cos diff=sympy.diff integrate=sympy.integratedef jin (fr1 ,fr2 ):f21 = fr1 * fr2 * (1 / r1) * fr1 * fr2 * r1 * r1 * r2 * r2f22 = fr1 * fr2 * (1 / r2) * fr1 * fr2 * r1 * r1 * r2 * r2f23 = (integrate(f21, (r2, 0, r1)))f24 = (integrate(f22, (r2, r1, float('inf'))))f25 = (16 * pi ** (2) * integrate(f24 + f23, (r1, 0, float('inf'))))# print("f23",f23)# print("f24",f24)print("J", f25)return f25def hin( fx1 ,fx2, z ):fx = fx1z=z# 拉普拉斯算符f1 = (1 / (r * r)) * diff((r * r * diff(fx, r)), r)f2 = (1 / (r * r * sin(θ))) * diff((sin(θ) * diff(fx, θ)), θ)f3 = (1 / (r * r * sin(θ) * sin(θ))) * diff(fx, Φ, Φ)f8 = fx2*(-1 / 2) * (f1 + f2 + f3)# print?? (?? f1 )# print?? (?? f2 )# print?? (?? f3 )#print??? ( f8 )# 球坐標(biāo)積分? 動能f9 = (integrate((integrate(integrate(f8 * r * r * sin(θ), (r, 0, float('inf'))), (θ, 0, pi))), (Φ, 0, 2 * pi)))print(f9)f10 = fx2 * (-z / r) * fx# 勢能#print(f10)f11 = (integrate((integrate(integrate(f10 * r * r * sin(θ), (r, 0, float('inf'))), (θ, 0, pi))), (Φ, 0, 2 * pi)))print(f11)print("H", f9 + f11)d=f9+f11str=f9,f11,dreturn strz=2.0f = open('d:/工業(yè)/f/naf3數(shù)據(jù)處理.csv','w',encoding='gbk') csv_writer = csv.writer(f)for i in range(1,200):a0=0.2+i*0.01fx1 = (z / a0) ** (1.5) * 2 * sympy.exp(-z * r / a0) * (4 * pi) ** (-0.5)fr1=(z/a0)**(1.5)*2*sympy.exp(-z*r1/a0? )*(4*pi)**(-0.5)fr2=(z/a0)**(1.5)*2*sympy.exp(-z*r2/a0? )*(4*pi)**(-0.5)d2=jin(fr1, fr2)d = hin(fx1, fx1, z)print(" i ", i ,"? ",a0,"? ",d ," ",d2)csv_writer.writerow([ a0 ,d ,d2])# 5. 關(guān)閉文件 f.close()

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