L Schrödinger’s Equation:

iℏ\frac{∂ψ}{∂t} = −\frac{ℏ^{2}}{2m}∇^{2}ψ + V ψ

M. Dirac Equation:

(i D̸ − m) ψ = 0

N. Atiyah-Singer Theorem for Twisted Dirac Operator:

dim ker / D_{E} − dim coker / D_{E} = ∫_{M} Â(M) · ch(E)