Eigenmath Demo

-- Exchange energy for two electrons in a box (10 seconds)

pi = float(pi) -- use numerical value of pi

-- base units

ampere = "ampere"
kilogram = "kilogram"
meter = "meter"
second = "second"

-- derived units

coulomb = ampere second
farad = ampere^2 kilogram^(-1) meter^(-2) second^4
joule = kilogram meter^2 second^(-2)
volt = ampere^(-1) kilogram meter^2 second^(-3)

-- physical constants

hbar = 1.054572 10^(-34) joule second      -- Planck's constant
epsilon0 = 8.854188 10^(-12) farad / meter -- electric constant
e = 1.602176 10^(-19) coulomb              -- elementary charge
me = 9.109382 10^(-31) kilogram            -- mass of electron
mp = 1.672622 10^(-27) kilogram            -- mass of proton

eV = 1/e coulomb "eV" / joule -- conversion constant

-- numerical integrator

N = 100

S(f) = (L/N)^2 sum(j,1,N,sum(k,1,N,
       test(j == k,0,eval(f,x,(j - 0.5) L/N,y,(k - 0.5) L/N))))

-- position basis for particle in a box

phi(n,x) = sqrt(2 / L) sin(n pi x / L)

"Length"

L = 1.0 10^(-9) meter
L

-- antisymmetrized wavefunction

psi = sqrt(1/2) (phi(1,x) phi(2,y) - phi(2,x) phi(1,y))

"Potential energy"

Vhat(psi) = psi e^2 / (4 pi epsilon0 abs((x - y) / meter) meter)

f = conj(psi) Vhat(psi)

V = S(f) eV
V

"Classical potential energy"

f = conj(phi(1,x) phi(2,y)) Vhat(phi(1,x) phi(2,y))

V0 = S(f) eV
V0

"Exchange energy"

V - V0