Fixing decay and blow-up mix-up in conn. formulas

src/wkb_bound.md

@@ -76,8 +76,8 @@ Below, we will see that the boundary conditions *(connection formulas)* impose c
     === "Positive slope"
         | $E > V(x)$ | $E < V(x)$ |
         | :-----------: | :-----------: |
-        | $$\frac{2C}{\sqrt{p(x)}} \sin\left( \frac{1}{\hbar} \int_x^{x_t} p(x') dx' + \frac{\pi}{4} \right)$$ | $$\frac{C}{\sqrt{\|p(x)\|}} e^{-\frac{1}{\hbar} \int_{x_t}^x \|p(x')\|dx'} \quad \text{ (blowing up)}$$ |
-        | $$\frac{D}{\sqrt{p(x)}} \cos\left( \frac{1}{\hbar} \int_x^{x_t} p(x') dx' + \frac{\pi}{4} \right)$$ | $$\frac{D}{\sqrt{\|p(x)\|}} e^{\frac{1}{\hbar} \int_{x_t}^x \|p(x')\|dx'} \quad \text{ (decaying)}$$ |
+        | $$\frac{2C}{\sqrt{p(x)}} \sin\left( \frac{1}{\hbar} \int_x^{x_t} p(x') dx' + \frac{\pi}{4} \right)$$ | $$\frac{C}{\sqrt{\|p(x)\|}} e^{-\frac{1}{\hbar} \int_{x_t}^x \|p(x')\|dx'} \quad \text{ (decaying)}$$ |
+        | $$\frac{D}{\sqrt{p(x)}} \cos\left( \frac{1}{\hbar} \int_x^{x_t} p(x') dx' + \frac{\pi}{4} \right)$$ | $$\frac{D}{\sqrt{\|p(x)\|}} e^{\frac{1}{\hbar} \int_{x_t}^x \|p(x')\|dx'} \quad \text{ (blowing up)}$$ |
         
     === "Negative slope"
 
@@ -125,8 +125,8 @@ Below, we will see that the boundary conditions *(connection formulas)* impose c
     === "Positive slope"
         | $E > V(x)$ | $E < V(x)$ |
         | :-----------: | :-----------: |
-        | $$\frac{2C}{\sqrt{p(x)}} \sin\left( \frac{1}{\hbar} \int_x^{x_t} p(x') dx' + \frac{\pi}{4} \right)$$ | $$\frac{C}{\sqrt{\|p(x)\|}} e^{-\frac{1}{\hbar} \int_{x_t}^x \|p(x')\|dx'} \quad \text{ (blowing up)}$$ |
-        | $$\frac{D}{\sqrt{p(x)}} \cos\left( \frac{1}{\hbar} \int_x^{x_t} p(x') dx' + \frac{\pi}{4} \right)$$ | $$\frac{D}{\sqrt{\|p(x)\|}} e^{\frac{1}{\hbar} \int_{x_t}^x \|p(x')\|dx'} \quad \text{ (decaying)}$$ |
+        | $$\frac{2C}{\sqrt{p(x)}} \sin\left( \frac{1}{\hbar} \int_x^{x_t} p(x') dx' + \frac{\pi}{4} \right)$$ | $$\frac{C}{\sqrt{\|p(x)\|}} e^{-\frac{1}{\hbar} \int_{x_t}^x \|p(x')\|dx'} \quad \text{ (decaying)}$$ |
+        | $$\frac{D}{\sqrt{p(x)}} \cos\left( \frac{1}{\hbar} \int_x^{x_t} p(x') dx' + \frac{\pi}{4} \right)$$ | $$\frac{D}{\sqrt{\|p(x)\|}} e^{\frac{1}{\hbar} \int_{x_t}^x \|p(x')\|dx'} \quad \text{ (blowing up)}$$ |
         
     === "Negative slope"