3D harmonic oscillator

[ohno]

3D isotropic harmonic oscillator on spherical coordinate system is already implemented as SphericalOscillator #7.

HarmonicOscillator3D is reserved for the name of this model. Please implement the anisotropic (general) 3D harmonic oscillator on Cartesian coordinate system. The spherical harmonics will not be used and a product of three Hermitian polynomials should be used for wavefunction. Refer to the well tested 1D harmonic oscillator:

Antique.jl/src/HarmonicOscillator.jl

Lines 1 to 34 in ac92c62

	export HarmonicOscillator, V, E, ψ, H
	@kwdef struct HarmonicOscillator
	k = 1.0
	m = 1.0
	ℏ = 1.0
	end
	function V(model::HarmonicOscillator, x)
	k = model.k
	return 1//2 * k * x^2
	end
	function E(model::HarmonicOscillator; n=0)
	k = model.k
	m = model.m
	ℏ = model.ℏ
	ω = sqrt(k/m)
	return ℏ * ω * (n+1//2)
	end
	function ψ(model::HarmonicOscillator, x; n=0)
	k = model.k
	m = model.m
	ℏ = model.ℏ
	ω = sqrt(k/m)
	A = sqrt(1//(factorial(n)*2^n)*sqrt(m*ω/(π*ℏ)))
	ξ = sqrt(m*ω/ℏ) * x
	return A * H(model,ξ,n=n) * exp(-ξ^2/2)
	end
	function H(model::HarmonicOscillator, x; n=0)
	return factorial(n) * sum(i -> (-1)^i // (factorial(i) * factorial(n-2*i)) * (2*x)^(n-2*i), 0:Int(floor(n/2)))
	end