PhysicsCircus

Hydrogen Molecules是2個Proton各別擁有1個electron。 IBM Account Info: 140.110.13.2/u00sam00/慣用密碼

syms r a lam mu positive
Phi=2*lam^(3/2)*exp(-lam*r)
PhiA=2*lam^(3/2)*exp(-lam*(r^2+a^2-2*r*a*mu)^(1/2))
Phi2A=2*lam^(3/2)*exp(-lam*(r^2+4*a^2-4*r*a*mu)^(1/2))
Saa=int(Phi*Phi*r*r,r,0,inf)
PhiABr=int(Phi*Phi2A, mu, -1, 1)/2
PhiABr=simplify(Phi2Ar)
Sab=int(PhiABr*r*r, r, 0, inf)
Sab=simplify(Sab)
N=1/2/(1+Sab)

dPhi=diff(Phi,r)
Kaa=int(dPhi*dPhi*r*r,r,0,inf)
dPhi2A=diff(Phi2A,r)
dPhi2A=simplify(dPhi2A)

Kab=int(dPhi*dPhi2A,mu,-1,1)/2
Kab=simplify(Kab)
Kab=int(Kab*r*r,r,0,inf)

K=Kaa+Kab

1s orbital

Atomic orbitals: 1s equations

The symbols used in the following are:

    * r = radius expressed in atomic units (1 Bohr radius = 52.9 pm)
    * π = 3.14159 approximately
    * e = 2.71828 approximately
    * Z = effective nuclear charge for that orbital in that atom.
    * ρ = 2Zr/n where n is the principal quantum number (1 for the 1s orbital)

Table of equations for the 1s orbital. Function  Equation
Radial wave function, R1s  = 2 × Z3/2 × e-ρ/2
Angular wave function, Y1s  = 1 × (1/4π)1/2
Wave function, ψ1s  = R1s × Y1s
 = 2Z3/2e-ρ/2 × (1/4π)1/2
Electron density  = ψ1s2
Radial distribution function  = 4πr2ψ1s2