\frac{QEq}{\hbar \omega}

Show wavefunctions

Scale = 0.5
α = 0.01 (slider from -0.5 to 0.5, step 0.01)
E1(x) = 1.5 - 0.5 * α^(2)
H2(x) = 4 * x^(2) - 2
H1(x) = 2 * x
H0(x) = 1
Coeff(n) = sqrt(2^(n) * n!)
Phi2(x) = H2(x) * ℯ^((-x^(2)) / 2) / Coeff(2)
Phi1(x) = H1(x) * ℯ^((-x^(2)) / 2) / Coeff(1)
Phi0(x) = H0(x) * ℯ^((-x^(2)) / 2) / Coeff(0)
H3(x) = 8 * x^(3) - 12 * x
H4(x) = 16 * x^(4) - 48 * x^(2) + 12
Phi3(x) = H3(x) * ℯ^((-x^(2)) / 2) / Coeff(3)
w = 0.1
V2(x) = -α * x
V(x) = 0.5 * x^(2) + V2(x)
E0(x) = 0.5 - 0.5 * α^(2)
E2(x) = 2.5 - 0.5 * α^(2)
Phi4(x) = H4(x) * ℯ^((-x^(2)) / 2) / Coeff(4)
Phi0u(x) = E0(x) + Scale * Phi0(x)
b = false
Phi1p(x) = E1(x) + Scale * (Phi1(x) - α / sqrt(2) * Phi0(x) + α * Phi2(x))
Phi0p(x) = E0(x) + Scale * (Phi0(x) + α / sqrt(2) * Phi1(x))
Phi2p(x) = E2(x) + Scale * (Phi2(x) - α * Phi1(x) + α * sqrt(3 / 2) * Phi3(x))
Phi2u(x) = E2(x) + Scale * Phi2(x)
Phi1u(x) = E1(x) + Scale * Phi1(x)
a = Integral(x * (Phi0p(x) - E0(x))^(2), -5, 5)
c = Integral(x * (Phi1p(x) - E1(x))^(2), -5, 5)
d = Integral(x * (Phi2p(x) - E2(x))^(2), -6, 6)
N0: Integral[Phi0(x)^(2), -6, 6] / sqrt(π)
x01: Integral[x * Phi0(x) * Phi1(x), -6, 6] / sqrt(π)
x12: Integral[x * Phi2(x) * Phi1(x), -6, 6] / sqrt(π)
x23: Integral[x * Phi2(x) * Phi3(x), -6, 6] / sqrt(π)