Add tests for MorsePotential and PoschlTeller, Close #43

ohno · Jun 9, 2024 · b33a273 · b33a273
1 parent d86080a
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Showing 7 changed files with 310 additions and 67 deletions.
diff --git a/src/MorsePotential.jl b/src/MorsePotential.jl
@@ -27,10 +27,9 @@ function V(model::MorsePotential, r)
 end
 
 # eigenvalues
-function E(model::MorsePotential; n::Int=0)
-  n_max = nₘₐₓ(model)
-  if !(0 ≤ n ≤ n_max)
-    throw(DomainError("n = $n, n_max = $n_max", "n must be non-negative and smaller than n_max: 0 ≤ n ≤ n_max."))
+function E(model::MorsePotential; n::Int=0, nocheck=false)
+  if !(0 ≤ n ≤ nₘₐₓ(model) || nocheck)
+    throw(DomainError("(n,nₘₐₓ(model)) = ($n,$(nₘₐₓ(model)))", "This function is defined for 0 ≤ n ≤ nₘₐₓ(model)."))
   end
   Dₑ = model.Dₑ
   k = model.k
@@ -52,9 +51,8 @@ end
 
 # eigenfunctions
 function ψ(model::MorsePotential, r; n::Int=0)
-  n_max = nₘₐₓ(model)
-  if !(0 ≤ n ≤ n_max)
-    throw(DomainError("n = $n, n_max = $n_max", "n must be non-negative and smaller than n_max: 0 ≤ n ≤ n_max."))
+  if !(0 ≤ n ≤ nₘₐₓ(model))
+    throw(DomainError("(n,nₘₐₓ(model)) = ($n,$(nₘₐₓ(model)))", "This function is defined for 0 ≤ n ≤ nₘₐₓ(model)."))
   end
   if !(0 ≤ r)
     throw(DomainError("r = $r", "r must be non-negative: 0 ≤ r."))

diff --git a/src/PoschlTeller.jl b/src/PoschlTeller.jl
@@ -21,10 +21,10 @@ function nₘₐₓ(model::PoschlTeller)
 end
 
 # eigenvalues
-function E(model::PoschlTeller; n::Int=0)
+function E(model::PoschlTeller; n::Int=0, nocheck=false)
   n_max = nₘₐₓ(model)
-  if !(0 ≤ n ≤ n_max)
-    throw(DomainError("(n,n_max) = ($n,$n_max)", "This function is defined for 0 ≤ n ≤ n_max."))
+  if !(0 ≤ n ≤ nₘₐₓ(model) || nocheck)
+    throw(DomainError("(n,nₘₐₓ(model)) = ($n,$(nₘₐₓ(model)))", "This function is defined for 0 ≤ n ≤ nₘₐₓ(model)."))
   end
   λ = model.λ
   m = model.m
@@ -37,8 +37,8 @@ end
 # eigenfunctions
 function ψ(model::PoschlTeller, x; n::Int=0)
   n_max = nₘₐₓ(model)
-  if !(0 ≤ n ≤ n_max)
-    throw(DomainError("(n,n_max) = ($n,$n_max)", "This function is defined for 0 ≤ n ≤ n_max."))
+  if !(0 ≤ n ≤ nₘₐₓ(model))
+    throw(DomainError("(n,nₘₐₓ(model)) = ($n,$(nₘₐₓ(model)))", "This function is defined for 0 ≤ n ≤ nₘₐₓ(model)."))
   end
   λ = model.λ
   mu = n_max - n + 1

diff --git a/test/MorsePotential.jl b/test/MorsePotential.jl
@@ -199,3 +199,57 @@ end
 
 println("""```
 """)
+
+
+# 0 < Eₙ₊₁ - Eₙ for 0 ≤ n ≤ nₘₐₓ
+
+
+println(raw"""
+#### Recurrence Relation between $E_{n+1}$ and $E_n$
+
+```math
+\begin{equation}
+\left\{ \,
+  \begin{aligned}
+    0 < \Delta E && 0 \leq n \leq n_\mathrm{max} \\
+    \Delta E < 0 && \mathrm{otherwise}
+  \end{aligned}
+\right.
+\end{equation}
+```
+
+```math
+\Delta E =  E_{n+1} - E_n
+```
+
+```math
+n_\mathrm{max} = \left\lfloor\frac{2 D_{\mathrm{e}}-h \nu_0}{h \nu_0}\right\rfloor
+```
+
+```""")
+
+@testset "0 < Eₙ₊₁ - Eₙ for 0 ≤ n ≤ nₘₐₓ" begin
+  println(" n  Eₙ          ΔE")
+  for n in 0:nₘₐₓ(MP)+5
+    Eₙ₊₁ = E(MP, n=n+1, nocheck=true)
+    Eₙ   = E(MP, n=n, nocheck=true)
+    ΔE  = Eₙ₊₁ - Eₙ
+    @printf("%2d  %+9.6f  %+9.6f  ", n, Eₙ, ΔE)
+    if n ≤ nₘₐₓ(MP)
+      print("0 < ΔE  ")
+      acceptance = 0 < ΔE
+    else
+      print("ΔE < 0  ")
+      acceptance = ΔE < 0
+    end
+    @test acceptance
+    println(acceptance ? "✔" : "✗")
+    if nₘₐₓ(MP) == n
+      println("-----------------------------------  nₘₐₓ(MP) = ", nₘₐₓ(MP))
+    end
+  end
+end
+
+println("""```
+""")
+
diff --git a/test/PoschlTeller.jl b/test/PoschlTeller.jl
@@ -152,8 +152,8 @@ are given by the sum of 2 Taylor series:
 
 @testset "∫ψₙ*Hψₙdx = <ψₙ|H|ψₙ> = Eₙ" begin
   ψHψ(PT, x; n=0, Δx=0.005) = V(PT,x)*ψ(PT,x,n=n)^2 - PT.ℏ^2/(2*PT.m)*conj(ψ(PT,x,n=n))*(ψ(PT,x+Δx,n=n)-2*ψ(PT,x,n=n)+ψ(PT,x-Δx,n=n))/Δx^2
-  println("  λ |  n |        analytical |         numerical ")
-  println("--- | -- | ----------------- | ----------------- ")
+  println("  λ |  n |   m |   ℏ |  x₀ |        analytical |         numerical ")
+  println("--- | -- | --- | --- | --- | ----------------- | ----------------- ")
   for λ in [1,2,3]
   for n in 0:λ-1
   for m in [1.0,exp(1)]
@@ -164,7 +164,7 @@ are given by the sum of 2 Taylor series:
     numerical  = quadgk(x -> ψHψ(PT, x, n=n, Δx=0.001), -Inf, Inf, atol=1e-4)[1]
     acceptance = iszero(analytical) ? isapprox(analytical, numerical, atol=1e-3) : isapprox(analytical, numerical, rtol=1e-5)
     @test acceptance
-    @printf("%.1f | %2d | %.1f |%.1f |%.1f |%17.12f | %17.12f %s\n", λ, n, m, ℏ, x₀, analytical, numerical, acceptance ? "✔" : "✗")
+    @printf("%.1f | %2d | %.1f | %.1f | %.1f |%17.12f | %17.12f %s\n", λ, n, m, ℏ, x₀, analytical, numerical, acceptance ? "✔" : "✗")
   end
   end
   end
@@ -174,4 +174,66 @@ end
 PT = PoschlTeller(λ=1.0, m=1.0, ℏ=1.0)
 
 println("""```
-""")
+""")
+
+
+# 0 < Eₙ₊₁ - Eₙ for 0 ≤ n ≤ nₘₐₓ
+
+
+println(raw"""
+#### Recurrence Relation between $E_{n+1}$ and $E_n$
+
+```math
+\begin{equation}
+\left\{ \,
+  \begin{aligned}
+    0 < \Delta E && 0 \leq n \leq n_\mathrm{max} \\
+    \Delta E < 0 && \mathrm{otherwise}
+  \end{aligned}
+\right.
+\end{equation}
+```
+
+```math
+\Delta E =  E_{n+1} - E_n
+```
+
+```math
+n_\mathrm{max} = \left\lfloor \lambda \right\rfloor - 1
+```
+
+```""")
+
+@testset "0 < Eₙ₊₁ - Eₙ for 0 ≤ n ≤ nₘₐₓ" begin
+  for PT in [
+    PoschlTeller(λ=2, m=1.0, ℏ=1.0, x₀=1.0),
+    PoschlTeller(λ=3, m=1.0, ℏ=1.0, x₀=1.0),
+    PoschlTeller(λ=4, m=1.0, ℏ=1.0, x₀=1.0),
+    PoschlTeller(λ=10, m=1.0, ℏ=1.0, x₀=1.0),
+  ]
+    @show PT
+    println(" n  Eₙ          ΔE")
+    for n in 0:nₘₐₓ(PT)+5
+      Eₙ₊₁ = E(PT, n=n+1, nocheck=true)
+      Eₙ   = E(PT, n=n, nocheck=true)
+      ΔE  = Eₙ₊₁ - Eₙ
+      @printf("%2d  %+9.6f  %+9.6f  ", n, Eₙ, ΔE)
+      if n ≤ nₘₐₓ(PT)
+        print("0 < ΔE  ")
+        acceptance = 0 < ΔE
+      else
+        print("ΔE < 0  ")
+        acceptance = ΔE < 0
+      end
+      @test acceptance
+      println(acceptance ? "✔" : "✗")
+      if n == nₘₐₓ(PT)
+        println("-----------------------------------  nₘₐₓ(PT) = ", nₘₐₓ(PT))
+      end
+    end
+    println()
+  end
+end
+
+println("""```
+""")
diff --git a/test/result/MorsePotential.log b/test/result/MorsePotential.log
@@ -887,4 +887,54 @@ are given by the sum of 2 Taylor series:
 0.1 |  9 |   -0.026741858566 |   -0.026742018376 ✔
 ```
 
+#### Recurrence Relation between $E_{n+1}$ and $E_n$
+
+```math
+\begin{equation}
+\left\{ \,
+  \begin{aligned}
+    0 < \Delta E && 0 \leq n \leq n_\mathrm{max} \\
+    \Delta E < 0 && \mathrm{otherwise}
+  \end{aligned}
+\right.
+\end{equation}
+```
+
+```math
+\Delta E =  E_{n+1} - E_n
+```
+
+```math
+n_\mathrm{max} = \left\lfloor\frac{2 D_{\mathrm{e}}-h \nu_0}{h \nu_0}\right\rfloor
+```
+
+```
+ n  Eₙ          ΔE
+ 0  -0.097414  +0.010033  0 < ΔE  ✔
+ 1  -0.087381  +0.009488  0 < ΔE  ✔
+ 2  -0.077893  +0.008943  0 < ΔE  ✔
+ 3  -0.068951  +0.008398  0 < ΔE  ✔
+ 4  -0.060553  +0.007852  0 < ΔE  ✔
+ 5  -0.052701  +0.007307  0 < ΔE  ✔
+ 6  -0.045393  +0.006762  0 < ΔE  ✔
+ 7  -0.038631  +0.006217  0 < ΔE  ✔
+ 8  -0.032414  +0.005672  0 < ΔE  ✔
+ 9  -0.026742  +0.005127  0 < ΔE  ✔
+10  -0.021615  +0.004582  0 < ΔE  ✔
+11  -0.017033  +0.004037  0 < ΔE  ✔
+12  -0.012996  +0.003492  0 < ΔE  ✔
+13  -0.009505  +0.002946  0 < ΔE  ✔
+14  -0.006558  +0.002401  0 < ΔE  ✔
+15  -0.004157  +0.001856  0 < ΔE  ✔
+16  -0.002301  +0.001311  0 < ΔE  ✔
+17  -0.000989  +0.000766  0 < ΔE  ✔
+18  -0.000223  +0.000221  0 < ΔE  ✔
+-----------------------------------  nₘₐₓ(MP) = 18
+19  -0.000002  -0.000324  ΔE < 0  ✔
+20  -0.000327  -0.000869  ΔE < 0  ✔
+21  -0.001196  -0.001414  ΔE < 0  ✔
+22  -0.002610  -0.001959  ΔE < 0  ✔
+23  -0.004570  -0.002505  ΔE < 0  ✔
+```
+