Simple Gaussian benchmark

calculations/MT-V.jl

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+# Malfliet–Tjon V (MT-V) — the standard few-body benchmark
+# Reference 2-body bound state: E₂ ≈ −0.41 MeV
+
+include("../Hamiltonian.jl")
+mode = cpu_tensor
+T = Float32 # single-precision mode
+
+V_R = 1458.05 # MeV·fm   
+μ_R = 3.11 # fm⁻¹
+V_A = -578.09 # MeV·fm 
+μ_A = 1.55 # fm⁻¹
+
+r2_reg = 0.000001 # fm², regularization parameter to avoid singularity at r=0
+V_MTV(r2) = V_R * exp(−μ_R * sqrt(r2))/sqrt(r2 + r2_reg)  +  V_A * exp(−μ_A * sqrt(r2))/sqrt(r2 + r2_reg)
+
+# ℏ²/m_N = 41.47 MeV·fm²   (m_N c² = 938.92 MeV)
+μ = (1 / 41.47) / 2
+
+ϕ = 0
+d = 3
+n = 2
+N = 80
+L = 20
+n_imag = 1
+
+s = system{T}(d, n, N, L, μ)
+H = Hamiltonian{T}(s, V_MTV, ϕ, n_imag, mode)
+@time evals, _, info = eig(H, 10, resonances = false)
+
+sort!(evals)
+display(evals[1:3])
+
+# Result incorrect and does not converge, most probably due to singularity at r=0

calculations/simple_gaussian.jl

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+# Simple Gaussian benchmark, with units
+# Expected 2-body bound state: E₂ ≈ -1.00 MeV
+
+include("../Hamiltonian.jl")
+mode = cpu_tensor
+T = Float32 # single-precision mode
+
+V_0 = -38.4671 # MeV
+r_0 = 2 # fm
+
+V_benchmark(r2) = V_0 * exp(−r2 / r_0^2)
+
+m_N = 939.565 # MeV/c²
+ħ = 197.327 # MeV·fm/c
+
+μ = (m_N / 2) / ħ^2
+
+ϕ = 0
+d = 3
+n = 2
+N = 80
+L = 40 # fm
+n_imag = 1
+
+s = system{T}(d, n, N, L, μ)
+H = Hamiltonian{T}(s, V_benchmark, ϕ, n_imag, mode)
+@time evals, _, info = eig(H, 3, resonances = false)
+
+sort!(evals)
+display(evals[1:3])
+
+# Result = -1.001821 MeV