Typo in morse potential documentation, dx -> dr for computing eigen e…

…nergy
ohno · May 19, 2024 · 83d2267 · 83d2267
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Showing 2 changed files with 8 additions and 8 deletions.
diff --git a/test/MorsePotential.jl b/test/MorsePotential.jl
@@ -122,10 +122,10 @@ println(raw"""
 ```math
   \begin{aligned}
     E_n
-    &=      \int \psi^\ast_n(r) \hat{H} \psi_n(r) \mathrm{d}x \\
-    &=      \int \psi^\ast_n(r) \left[ \hat{V} + \hat{T} \right] \psi(r) \mathrm{d}x \\
-    &=      \int \psi^\ast_n(r) \left[ V(r) - \frac{\hbar^2}{2m} \frac{\mathrm{d}^{2}}{\mathrm{d} r^{2}} \right] \psi(r) \mathrm{d}x \\
-    &\simeq \int \psi^\ast_n(r) \left[ V(r)\psi(r) -\frac{\hbar^2}{2m} \frac{\psi(r+\Delta r) - 2\psi(r) + \psi(r-\Delta r)}{\Delta r^{2}} \right] \mathrm{d}x.
+    &=      \int \psi^\ast_n(r) \hat{H} \psi_n(r) \mathrm{d}r \\
+    &=      \int \psi^\ast_n(r) \left[ \hat{V} + \hat{T} \right] \psi(r) \mathrm{d}r \\
+    &=      \int \psi^\ast_n(r) \left[ V(r) - \frac{\hbar^2}{2m} \frac{\mathrm{d}^{2}}{\mathrm{d} r^{2}} \right] \psi(r) \mathrm{d}r \\
+    &\simeq \int \psi^\ast_n(r) \left[ V(r)\psi(r) -\frac{\hbar^2}{2m} \frac{\psi(r+\Delta r) - 2\psi(r) + \psi(r-\Delta r)}{\Delta r^{2}} \right] \mathrm{d}r.
   \end{aligned}
 ```
 

diff --git a/test/result/MorsePotential.log b/test/result/MorsePotential.log
@@ -785,10 +785,10 @@
 ```math
   \begin{aligned}
     E_n
-    &=      \int \psi^\ast_n(r) \hat{H} \psi_n(r) \mathrm{d}x \\
-    &=      \int \psi^\ast_n(r) \left[ \hat{V} + \hat{T} \right] \psi(r) \mathrm{d}x \\
-    &=      \int \psi^\ast_n(r) \left[ V(r) - \frac{\hbar^2}{2m} \frac{\mathrm{d}^{2}}{\mathrm{d} r^{2}} \right] \psi(r) \mathrm{d}x \\
-    &\simeq \int \psi^\ast_n(r) \left[ V(r)\psi(r) -\frac{\hbar^2}{2m} \frac{\psi(r+\Delta r) - 2\psi(r) + \psi(r-\Delta r)}{\Delta r^{2}} \right] \mathrm{d}x.
+    &=      \int \psi^\ast_n(r) \hat{H} \psi_n(r) \mathrm{d}r \\
+    &=      \int \psi^\ast_n(r) \left[ \hat{V} + \hat{T} \right] \psi(r) \mathrm{d}r \\
+    &=      \int \psi^\ast_n(r) \left[ V(r) - \frac{\hbar^2}{2m} \frac{\mathrm{d}^{2}}{\mathrm{d} r^{2}} \right] \psi(r) \mathrm{d}r \\
+    &\simeq \int \psi^\ast_n(r) \left[ V(r)\psi(r) -\frac{\hbar^2}{2m} \frac{\psi(r+\Delta r) - 2\psi(r) + \psi(r-\Delta r)}{\Delta r^{2}} \right] \mathrm{d}r.
   \end{aligned}
 ```