For the cubic 3D infinite well wave function
$ψ (x, y, z) = A s i n \frac{n_{x} π x}{L} s i n \frac{n_{y} π y}{L} s i n \frac{n_{z} π z}{L}$ show that the correct normalization constant is $A = {(2 / L)}^{3 / 2}$ .

Question

For the cubic 3D infinite well wave function
$ψ (x, y, z) = A s i n \frac{n_{x} π x}{L} s i n \frac{n_{y} π y}{L} s i n \frac{n_{z} π z}{L}$ show that the correct normalization constant is $A = {(2 / L)}^{3 / 2}$ .

Accepted Answer

The normalization constant is ${(\frac{2}{L})}^{3 / 2}$ .

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Short Answer

For the cubic 3D infinite well wave function
$ψ (x, y, z) = A s i n \frac{n_{x} π x}{L} s i n \frac{n_{y} π y}{L} s i n \frac{n_{z} π z}{L}$ show that the correct normalization constant is $A = {(2 / L)}^{3 / 2}$ .

Step by Step Solution

Step 1: Given data

Step 2: Normalization condition

Step 3: To determine the normalization constant

Step 4: Conclusion

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Modern Physics

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Short Answer

For the cubic 3D infinite well wave functionψ(x,y,z)=AsinnxπxLsinnyπyLsinnzπzL show that the correct normalization constant is A=(2/L)3/2.

Step by Step Solution

Step 1: Given data

Step 2: Normalization condition

Step 3: To determine the normalization constant

Step 4: Conclusion

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For the cubic 3D infinite well wave function
$ψ (x, y, z) = A s i n \frac{n_{x} π x}{L} s i n \frac{n_{y} π y}{L} s i n \frac{n_{z} π z}{L}$ show that the correct normalization constant is $A = {(2 / L)}^{3 / 2}$ .