"Exercise 4." e = 1.602176634 10^(-19) coulomb -- elementary charge h = 6.62607015 10^(-34) joule second -- Planck constant hbar = h / float(2 pi) -- reduced Planck constant electronvolt = e joule / coulomb joule = kilogram meter^2 / second^2 kilogram = "kilogram" meter = "meter" second = "second" m = 6.64 10^(-27) kilogram V = 1 electronvolt L = 10^(-6) meter omega = sqrt(2 V / m) / L omega psi(n) = C(n) exp(-m omega x^2 / (2 hbar)) H(n, x sqrt(m omega / hbar)) C(n) = 1 / sqrt(2^n n!) (m omega / (pi hbar))^(1/4) H(n,y,z) = (-1)^n exp(y^2) eval(d(exp(-z^2),z,n),z,y) Psi = (psi(2) + psi(3)) / sqrt(2) infty = 100.0 meter xbar = float(defint(x conj(Psi) Psi, x, -infty, infty)) xbar Hhat(f) = phat(phat(f)) / (2 m) + V f phat(f) = -i hbar d(f,x) V = m omega^2 x^2 / 2 Ebar = float(defint(conj(Psi) Hhat(Psi), x, -infty, infty)) Ebar = Ebar / electronvolt "electronvolt" -- convert joule to electronvolt Ebar E(n) = hbar omega (n + 1/2) "Expected eigenvalue" 1/2 (E(2) + E(3)) / electronvolt "electronvolt"
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