Research proof index

If f₀ is a function of (inner ℝ x s - c * t), the fderiv of its components with respect to spatial coordinates is equal to the corresponding component of the propagation direction s times time derivative.

The cost of f >>= g is roughly f.cost + g.cost

query' costs one query, plus the rest

Construct a canonical polynomial from a coefficient function Fin n → R. The coefficients are stored in an array (index i gives the coefficient of X^i) and then trimmed to remove trailing zeros. -/ def ofFn [Zero R] [BEq R] [LawfulBEq R] {n : ℕ} (f : Fin n → R) : CPolynomial R := ⟨(Raw.mk (Array.ofFn f)).trim, Raw.Trim.isCanonical_trim _⟩ section Div...

The energy eigenstates of the tight binding chain are orthogonal. This is a fundamental quantum mechanical result: eigenstates of a Hermitian operator (the Hamiltonian) with distinct eigenvalues are orthogonal. Here we prove it directly using the periodic boundary conditions which quantize the wavenumbers. The key physical insight is that different wavenu...

The energy eigenstates satisfy the time-independent Schrodinger equation.