diff --git a/FullShell/Manifest.toml b/FullShell/Manifest.toml
new file mode 100644
index 0000000..35ecc19
--- /dev/null
+++ b/FullShell/Manifest.toml
@@ -0,0 +1,451 @@
+# This file is machine-generated - editing it directly is not advised
+
+julia_version = "1.9.4"
+manifest_format = "2.0"
+project_hash = "6d11c8b2e2145583bdd4d7db14bb5f271c84edb3"
+
+[[deps.Adapt]]
+deps = ["LinearAlgebra", "Requires"]
+git-tree-sha1 = "6a55b747d1812e699320963ffde36f1ebdda4099"
+uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
+version = "4.0.4"
+weakdeps = ["StaticArrays"]
+
+    [deps.Adapt.extensions]
+    AdaptStaticArraysExt = "StaticArrays"
+
+[[deps.ArgTools]]
+uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
+version = "1.1.1"
+
+[[deps.ArnoldiMethod]]
+deps = ["LinearAlgebra", "Random", "StaticArrays"]
+git-tree-sha1 = "d57bd3762d308bded22c3b82d033bff85f6195c6"
+uuid = "ec485272-7323-5ecc-a04f-4719b315124d"
+version = "0.4.0"
+
+[[deps.Arpack]]
+deps = ["Arpack_jll", "Libdl", "LinearAlgebra", "Logging"]
+git-tree-sha1 = "9b9b347613394885fd1c8c7729bfc60528faa436"
+uuid = "7d9fca2a-8960-54d3-9f78-7d1dccf2cb97"
+version = "0.5.4"
+
+[[deps.Arpack_jll]]
+deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "OpenBLAS_jll", "Pkg"]
+git-tree-sha1 = "5ba6c757e8feccf03a1554dfaf3e26b3cfc7fd5e"
+uuid = "68821587-b530-5797-8361-c406ea357684"
+version = "3.5.1+1"
+
+[[deps.Artifacts]]
+uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
+
+[[deps.Base64]]
+uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
+
+[[deps.ChainRulesCore]]
+deps = ["Compat", "LinearAlgebra"]
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+uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+version = "1.23.0"
+weakdeps = ["SparseArrays"]
+
+    [deps.ChainRulesCore.extensions]
+    ChainRulesCoreSparseArraysExt = "SparseArrays"
+
+[[deps.Compat]]
+deps = ["TOML", "UUIDs"]
+git-tree-sha1 = "c955881e3c981181362ae4088b35995446298b80"
+uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
+version = "4.14.0"
+weakdeps = ["Dates", "LinearAlgebra"]
+
+    [deps.Compat.extensions]
+    CompatLinearAlgebraExt = "LinearAlgebra"
+
+[[deps.CompilerSupportLibraries_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
+version = "1.0.5+0"
+
+[[deps.DataStructures]]
+deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
+git-tree-sha1 = "1d0a14036acb104d9e89698bd408f63ab58cdc82"
+uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
+version = "0.18.20"
+
+[[deps.Dates]]
+deps = ["Printf"]
+uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
+
+[[deps.DelimitedFiles]]
+deps = ["Mmap"]
+git-tree-sha1 = "9e2f36d3c96a820c678f2f1f1782582fcf685bae"
+uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"
+version = "1.9.1"
+
+[[deps.Dictionaries]]
+deps = ["Indexing", "Random", "Serialization"]
+git-tree-sha1 = "35b66b6744b2d92c778afd3a88d2571875664a2a"
+uuid = "85a47980-9c8c-11e8-2b9f-f7ca1fa99fb4"
+version = "0.4.2"
+
+[[deps.Distances]]
+deps = ["LinearAlgebra", "Statistics", "StatsAPI"]
+git-tree-sha1 = "66c4c81f259586e8f002eacebc177e1fb06363b0"
+uuid = "b4f34e82-e78d-54a5-968a-f98e89d6e8f7"
+version = "0.10.11"
+weakdeps = ["ChainRulesCore", "SparseArrays"]
+
+    [deps.Distances.extensions]
+    DistancesChainRulesCoreExt = "ChainRulesCore"
+    DistancesSparseArraysExt = "SparseArrays"
+
+[[deps.Distributed]]
+deps = ["Random", "Serialization", "Sockets"]
+uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
+
+[[deps.DocStringExtensions]]
+deps = ["LibGit2"]
+git-tree-sha1 = "2fb1e02f2b635d0845df5d7c167fec4dd739b00d"
+uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
+version = "0.9.3"
+
+[[deps.Downloads]]
+deps = ["ArgTools", "FileWatching", "LibCURL", "NetworkOptions"]
+uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"
+version = "1.6.0"
+
+[[deps.ExprTools]]
+git-tree-sha1 = "27415f162e6028e81c72b82ef756bf321213b6ec"
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+version = "0.1.10"
+
+[[deps.FileWatching]]
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+
+[[deps.FrankenTuples]]
+git-tree-sha1 = "45f2d31d22d8bf962eaab74cf800127b4d307c61"
+uuid = "7e584817-dab4-53a9-9a51-4037a36b0ad0"
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+
+[[deps.FunctionWrappers]]
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+
+[[deps.GPUArraysCore]]
+deps = ["Adapt"]
+git-tree-sha1 = "ec632f177c0d990e64d955ccc1b8c04c485a0950"
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+
+[[deps.Indexing]]
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+uuid = "313cdc1a-70c2-5d6a-ae34-0150d3930a38"
+version = "1.1.1"
+
+[[deps.InteractiveUtils]]
+deps = ["Markdown"]
+uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
+
+[[deps.IntervalTrees]]
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+
+[[deps.IrrationalConstants]]
+git-tree-sha1 = "630b497eafcc20001bba38a4651b327dcfc491d2"
+uuid = "92d709cd-6900-40b7-9082-c6be49f344b6"
+version = "0.2.2"
+
+[[deps.JLLWrappers]]
+deps = ["Artifacts", "Preferences"]
+git-tree-sha1 = "7e5d6779a1e09a36db2a7b6cff50942a0a7d0fca"
+uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
+version = "1.5.0"
+
+[[deps.KrylovKit]]
+deps = ["ChainRulesCore", "GPUArraysCore", "LinearAlgebra", "Printf", "VectorInterface"]
+git-tree-sha1 = "3f3a92bbe8f568b689a7f7bc193f7c717d793751"
+uuid = "0b1a1467-8014-51b9-945f-bf0ae24f4b77"
+version = "0.7.1"
+
+[[deps.LibCURL]]
+deps = ["LibCURL_jll", "MozillaCACerts_jll"]
+uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21"
+version = "0.6.4"
+
+[[deps.LibCURL_jll]]
+deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll", "Zlib_jll", "nghttp2_jll"]
+uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0"
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+
+[[deps.LibGit2]]
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+uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"
+
+[[deps.LibSSH2_jll]]
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+
+[[deps.Libdl]]
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+
+[[deps.LinearAlgebra]]
+deps = ["Libdl", "OpenBLAS_jll", "libblastrampoline_jll"]
+uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+
+[[deps.LinearMaps]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "9948d6f8208acfebc3e8cf4681362b2124339e7e"
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+version = "3.11.2"
+weakdeps = ["ChainRulesCore", "SparseArrays", "Statistics"]
+
+    [deps.LinearMaps.extensions]
+    LinearMapsChainRulesCoreExt = "ChainRulesCore"
+    LinearMapsSparseArraysExt = "SparseArrays"
+    LinearMapsStatisticsExt = "Statistics"
+
+[[deps.LogExpFunctions]]
+deps = ["DocStringExtensions", "IrrationalConstants", "LinearAlgebra"]
+git-tree-sha1 = "18144f3e9cbe9b15b070288eef858f71b291ce37"
+uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
+version = "0.3.27"
+
+    [deps.LogExpFunctions.extensions]
+    LogExpFunctionsChainRulesCoreExt = "ChainRulesCore"
+    LogExpFunctionsChangesOfVariablesExt = "ChangesOfVariables"
+    LogExpFunctionsInverseFunctionsExt = "InverseFunctions"
+
+    [deps.LogExpFunctions.weakdeps]
+    ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+    ChangesOfVariables = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0"
+    InverseFunctions = "3587e190-3f89-42d0-90ee-14403ec27112"
+
+[[deps.Logging]]
+uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
+
+[[deps.Markdown]]
+deps = ["Base64"]
+uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
+
+[[deps.MbedTLS_jll]]
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+version = "2.28.2+0"
+
+[[deps.Mmap]]
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+
+[[deps.MozillaCACerts_jll]]
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+version = "2022.10.11"
+
+[[deps.NearestNeighbors]]
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+[[deps.NetworkOptions]]
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+[[deps.OpenBLAS_jll]]
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+
+[[deps.OpenLibm_jll]]
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+
+[[deps.OpenSpecFun_jll]]
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+[[deps.OrderedCollections]]
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+[[deps.Parameters]]
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+
+[[deps.Pkg]]
+deps = ["Artifacts", "Dates", "Downloads", "FileWatching", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"]
+uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
+version = "1.9.2"
+
+[[deps.PrecompileTools]]
+deps = ["Preferences"]
+git-tree-sha1 = "5aa36f7049a63a1528fe8f7c3f2113413ffd4e1f"
+uuid = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
+version = "1.2.1"
+
+[[deps.Preferences]]
+deps = ["TOML"]
+git-tree-sha1 = "9306f6085165d270f7e3db02af26a400d580f5c6"
+uuid = "21216c6a-2e73-6563-6e65-726566657250"
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+
+[[deps.Printf]]
+deps = ["Unicode"]
+uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
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+[[deps.ProgressMeter]]
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+git-tree-sha1 = "763a8ceb07833dd51bb9e3bbca372de32c0605ad"
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+version = "1.10.0"
+
+[[deps.QuadGK]]
+deps = ["DataStructures", "LinearAlgebra"]
+git-tree-sha1 = "9b23c31e76e333e6fb4c1595ae6afa74966a729e"
+uuid = "1fd47b50-473d-5c70-9696-f719f8f3bcdc"
+version = "2.9.4"
+
+[[deps.Quantica]]
+deps = ["ArnoldiMethod", "Arpack", "Compat", "DelimitedFiles", "Dictionaries", "ExprTools", "FrankenTuples", "FunctionWrappers", "IntervalTrees", "KrylovKit", "LinearAlgebra", "LinearMaps", "NearestNeighbors", "ProgressMeter", "QuadGK", "Random", "SparseArrays", "SpecialFunctions", "StaticArrays", "Statistics", "SuiteSparse"]
+git-tree-sha1 = "4103436d3ff5925e2bb0f78e2d98356e1b341331"
+repo-rev = "master"
+repo-url = "https://github.com/pablosanjose/Quantica.jl.git"
+uuid = "ae5ea0c6-3f5e-46a2-bc28-a7c4c7a4773c"
+version = "1.1.0"
+
+    [deps.Quantica.extensions]
+    QuanticaMakieExt = "Makie"
+
+    [deps.Quantica.weakdeps]
+    GeometryBasics = "5c1252a2-5f33-56bf-86c9-59e7332b4326"
+    Makie = "ee78f7c6-11fb-53f2-987a-cfe4a2b5a57a"
+
+[[deps.REPL]]
+deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"]
+uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
+
+[[deps.Random]]
+deps = ["SHA", "Serialization"]
+uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+
+[[deps.Requires]]
+deps = ["UUIDs"]
+git-tree-sha1 = "838a3a4188e2ded87a4f9f184b4b0d78a1e91cb7"
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+
+[[deps.SHA]]
+uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
+version = "0.7.0"
+
+[[deps.Serialization]]
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+
+[[deps.Sockets]]
+uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
+
+[[deps.SparseArrays]]
+deps = ["Libdl", "LinearAlgebra", "Random", "Serialization", "SuiteSparse_jll"]
+uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+
+[[deps.SpecialFunctions]]
+deps = ["IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
+git-tree-sha1 = "e2cfc4012a19088254b3950b85c3c1d8882d864d"
+uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
+version = "2.3.1"
+weakdeps = ["ChainRulesCore"]
+
+    [deps.SpecialFunctions.extensions]
+    SpecialFunctionsChainRulesCoreExt = "ChainRulesCore"
+
+[[deps.StaticArrays]]
+deps = ["LinearAlgebra", "PrecompileTools", "Random", "StaticArraysCore"]
+git-tree-sha1 = "bf074c045d3d5ffd956fa0a461da38a44685d6b2"
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+weakdeps = ["ChainRulesCore", "Statistics"]
+
+    [deps.StaticArrays.extensions]
+    StaticArraysChainRulesCoreExt = "ChainRulesCore"
+    StaticArraysStatisticsExt = "Statistics"
+
+[[deps.StaticArraysCore]]
+git-tree-sha1 = "36b3d696ce6366023a0ea192b4cd442268995a0d"
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+
+[[deps.SuiteSparse_jll]]
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+[[deps.Tar]]
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+[[deps.UUIDs]]
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+[[deps.Unicode]]
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+
+[[deps.Zlib_jll]]
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+uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
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+
+[[deps.libblastrampoline_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
+version = "5.8.0+0"
+
+[[deps.nghttp2_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
+version = "1.52.0+1"
+
+[[deps.p7zip_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
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diff --git a/FullShell/Project.toml b/FullShell/Project.toml
new file mode 100644
index 0000000..a9ac9d4
--- /dev/null
+++ b/FullShell/Project.toml
@@ -0,0 +1,3 @@
+[deps]
+Parameters = "d96e819e-fc66-5662-9728-84c9c7592b0a"
+Quantica = "ae5ea0c6-3f5e-46a2-bc28-a7c4c7a4773c"
diff --git a/src/FullShell.jl b/src/FullShell.jl
index c45da4e..0a4d551 100644
--- a/src/FullShell.jl
+++ b/src/FullShell.jl
@@ -1,5 +1,14 @@
 module FullShell
 
-# Write your package code here.
+using Quantica 
+using Parameters
+
+export build_cyl, ΣS3DUsadel, pairbreaking
+
+export σ0τx, σ0τy, σ0τz, σ0τ0, σzτ0, σzτz, σyτy, σyτz, σyτ0, σxτz, σxτ0, σ0, σx, σy, σz
+
+include("utilities/LP_usadel.jl")
+include("utilities/pauli_products.jl") 
+include("HamiltonianBuilder.jl")
 
 end
diff --git a/src/HamiltonianBuilder.jl b/src/HamiltonianBuilder.jl
new file mode 100755
index 0000000..62d7355
--- /dev/null
+++ b/src/HamiltonianBuilder.jl
@@ -0,0 +1,88 @@
+
+@with_kw struct Params @deftype Float64 #Units: nm, meV
+    ħ2ome = 76.1996
+    μBΦ0 = 119.6941183                  #Bohr magneton times magnetic flux quantum
+    m0 = 0.023
+    g = 12
+    P = 919.7                           #Bulck SOC parameters
+    Δg = 417  
+    Δs = 390  
+    preα = P^2/3 * (1/Δg^2 - 1/(Δg + Δs)^2)  #α = preα \times Rashba things
+    a0 = 5
+    t = ħ2ome/(2m0*a0^2)
+    echarge = 1
+    R = 70                              #radius of the cylinder
+    w = 10                              #width of the semiconductor
+    d = 10                              #wdith of the superconductor
+    Vmax = 0                            #dome profile parameters
+    Vmin = 0
+    Vexponent = 2
+    Δ0::ComplexF64 = 0.2 
+    ξd = 70 
+    α = 0                               #parameter defaults
+    μ = 0
+    τΓ = 1
+    Φ = 1                               #flux normalized to the flux quantum always
+end
+
+# Hamiltonian constructor 
+
+ΣS3DUsadel(Δ0, Λ, ω;) = -(uUsadel(Δ0, Λ, ω) * σ0τ0 - σ0τx) / sqrt(complex(1-uUsadel(Δ0, Λ, ω)^2))
+
+build_cyl(; nforced = nothing, MHC = true, kw...) = build_cyl(Params(; kw...); nforced, MHC)
+
+function build_cyl(p::Params; nforced = nothing, MHC = true)
+    @unpack μBΦ0, m0, g, preα, a0, t, echarge, R, w, d, Vmax, Vmin, Vexponent, Δ0, ξd, α, μ, τΓ, Φ = p 
+
+    # Lattice
+
+    R = floor(R/a0)*a0
+    lat = if MHC
+            Rav = R - w/2
+            LP.square(; a0) |> supercell((1, 0)) |> Quantica.transform!(r -> r + SA[0, Rav])
+          else
+            LP.square(; a0) |> supercell((1, 0), region = r -> max(a0, R - w) <= r[2] <= R)
+          end
+
+    # Model
+
+    # Kinetic term
+    p2 = @onsite((r; μ = μ) -> σ0τz *(t * ifelse(r[2] ≈ a0, 2.0 + 1.5, 2.0 + 2.0*!MHC) - μ)) + hopping((r, dr) -> -t * σ0τz * ifelse(iszero(dr[1]), r[2]/sqrt(r[2]^2 - 0.25*dr[2]^2), 1); range = a0)
+
+    # Dome profile
+    V(ρ, v0, v1) = v0 + (v1 - v0) * (ρ/R)^Vexponent
+    dϕ(ρ, v0, v1) = - (Vexponent/R) * (v1 - v0) * (ρ/R)^(Vexponent - 1) # ϕ = -V
+    potential = @onsite((r; Vmax = Vmax, Vmin = Vmin) -> σ0τz * V(r[2], Vmax, Vmin))
+
+    # Linear SOC
+    rashba = @hopping((r, dr; α = α, preα = preα, Vmin = Vmin, Vmax = Vmax) -> (α + preα * dϕ(r[2], Vmax, Vmin)) * (im * dr[1] / (2 * a0^2)) * σyτz; range = a0)
+
+    # g - Zeeman
+    zeeman = @onsite((; Φ = Φ) -> σzτ0 * 0.5 * g * μBΦ0 * Φ / area_LP)
+
+    # Magnetic field
+    area_LP = π * (R + d/2)^2 
+    eAφ(r, Φ) = echarge * 0.5 * π * Φ * r[2] / area_LP
+    n(Φ) = ifelse(nforced === nothing, round(Int, Φ), nforced)
+    mJ(Z, Φ) = Z + ifelse(iseven(n(Φ)), 0.5, 0.0)
+    J(Z, Φ) = mJ(Z, Φ) * σ0τ0 - 0.5 * σzτ0 - 0.5 * n(Φ) * σ0τz 
+    gauge = @onsite((r; Φ = Φ, Z = 0, α = α, preα = preα, Vmax = Vmax, Vmin = Vmin) ->
+          σ0τz * (σ0τz * eAφ(r, Φ) + J(Z, Φ) / r[2])^2 * t * a0^2 -
+          σzτz * (σ0τz * eAφ(r, Φ) + J(Z, Φ) / r[2]) * (α + preα * dϕ(r[2], Vmax, Vmin)) 
+    ) 
+
+    # SM hamiltonian 
+
+    hSM = lat |> hamiltonian(p2 + potential + rashba + zeeman + gauge; orbitals = Val(4))
+
+    # Superconductor
+    Λ(Φ) = pairbreaking(Φ, n(Φ), Δ0, ξd, R, d)
+    ΣS! = @onsite!((o, r; ω = 0, Φ = Φ, τΓ = τΓ) ->
+          o + τΓ * Δ0 * ΣS3DUsadel(Δ0, Λ(Φ), ω);
+          region = MHC ? Returns(true) : r -> r[2] > R - a0/2
+    )
+
+    hSC = hSM |> ΣS!
+
+    return hSM, hSC, p
+end
\ No newline at end of file
diff --git a/src/utilities/LP_usadel.jl b/src/utilities/LP_usadel.jl
new file mode 100644
index 0000000..ca03d31
--- /dev/null
+++ b/src/utilities/LP_usadel.jl
@@ -0,0 +1,16 @@
+function pairbreaking(Φ, n, Δ0, ξd, R, d)
+    RLP = R + d/2
+    Λ = ξd^2 * Δ0 / (1.76 * π * RLP^2) * (4 * (Φ - n)^2 + d^2 / RLP^2 * (Φ^2 + (n^2)/3))
+    return Λ
+end
+
+function uUsadel(Δ0, Λ, ω)
+    Δd = Δ0 * (1 - π/4 * Λ/Δ0 - π^2/32 * (Λ/Δ0)^2 - π^3/96 * (Λ/Δ0)^3)
+    pep = complex(-Δd^6 + 3 * Δd^4 * (Λ^2 + ω^2) + (Λ^2 + ω^2)^3 - 3 * Δd^2 * (Λ^4 - 16 * Λ^2 * ω^2 + ω^4) + 
+    6 * Δd * Λ * sqrt(complex(-3*(Δd^2 - Λ^2)^3 * ω^2 + 9 * (Δd^4 + 7 * Δd^2 * Λ^2 + Λ^4) * ω^4 + 9 * (-Δd^2 + Λ^2) * ω^6 + 3 * ω^8)))^(1/3)
+    nun = ω^2 - Δd^2 + Λ^2
+    rai = sqrt(complex(ω^2 - 2 * nun / 3 + nun^2 / (3 * pep) + pep / 3))
+    usa = 1/(2 * Δd) *(ω + sign(ω) * rai - sign(ω) * sqrt(complex(2 * ω^2 - 4 * nun/3 - nun^2 /(3 * pep) - pep/ 3 - sign(ω) * 2 * (Δd^2 + Λ^2) * ω / rai)))
+    return usa
+end
+
diff --git a/src/utilities/pauli_products.jl b/src/utilities/pauli_products.jl
new file mode 100644
index 0000000..6c5eb22
--- /dev/null
+++ b/src/utilities/pauli_products.jl
@@ -0,0 +1,15 @@
+const σ0τx = @SMatrix[0 0 1 0; 0 0 0 1; 1 0 0 0; 0 1 0 0]
+const σ0τy = @SMatrix[0 0 -im 0; 0 0 0 -im; im 0 0 0; 0 im 0 0]
+const σ0τz = @SMatrix[1 0 0 0; 0 1 0 0; 0 0 -1 0; 0 0 0 -1]
+const σ0τ0 = @SMatrix[1 0 0 0; 0 1 0 0; 0 0 1 0; 0 0 0 1]
+const σzτ0 = @SMatrix[1 0 0 0; 0 -1 0 0; 0 0 1 0; 0 0 0 -1]
+const σzτz = @SMatrix[1 0 0 0; 0 -1 0 0; 0 0 -1 0; 0 0 0 1]
+const σyτy = @SMatrix[0 0 0 -1; 0 0 1 0; 0 1 0 0; -1 0 0 0]
+const σyτz = @SMatrix[0 -im 0 0; im 0 0 0; 0 0 0 im; 0 0 -im 0]
+const σyτ0 = @SMatrix[0 -im 0 0; im 0 0 0; 0 0 0 -im; 0 0 im 0]
+const σxτz = @SMatrix[0 1 0 0; 1 0 0 0; 0 0 0 -1; 0 0 -1 0]
+const σxτ0 = @SMatrix[0 1 0 0; 1 0 0 0; 0 0 0 1; 0 0 1 0]
+const σ0 = SA[1 0; 0 1]
+const σx = SA[0 1; 1 0]
+const σy = SA[0 -im; im 0]
+const σz = SA[1 0; 0 -1];
\ No newline at end of file
diff --git a/test/runtests.jl b/test/runtests.jl
index b1f1e57..4b2fcf7 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -2,5 +2,5 @@ using FullShell
 using Test
 
 @testset "FullShell.jl" begin
-    # Write your tests here.
+    
 end