Search results with tag "The spherical harmonics"
Legendre Polynomials - Lecture 8 - University of Houston
nsmn1.uh.edul, which are the spherical harmonics; Y0 0 = p 1/(4π) Y1 1 = − p 3/(8π)sin(θ)eiφ Y1 −1 = p 3/(8π)sin(θ)e−iφ Y1 0 = p 3/(4π)cos(θ) Note that Ym∗ l = −Y −m l. The functions, Y m l (θ,φ), are the spherical harmonics, and we will later identify the operator, L, as proportional to the angular momentum operator in Quantum ...
6 Wave equation in spherical polar coordinates
www2.ph.ed.ac.ukThe spherical harmonics satisfy an orthogonality relation: * 2π 0 dφ * π 0 dθ sinθ, Ym1 l1 (θ,φ)-∗ Ym2 l2 (θ,φ)=δ l1,l2 δ m1,m2. Note that they are orthonormal, not just orthogonal, as the constant multiplying the product of Kronecker deltas is unity. 6.3.1 Completeness and the …
The SphericalHarmonics - Welcome to SCIPP
scipp.ucsc.edu2. The spherical harmonics In obtaining the solutions to Laplace’s equation in spherical coordinates, it is traditional to introduce the spherical harmonics, Ym ℓ (θ,φ), Ym ℓ (θ,φ) = (−1)m s