Show that its squar integrable

[leonne]

Homework Statement

This is a physics problem but don't understand the math really
f(x)=a(e^ix+ie^-x2

Homework Equations

∫f^*f =1

The Attempt at a Solution

I thought it would be f²=a(e^ix+ie^-x2)*a(e^ix+ie^-x2)
but they have it as a^*(e^-ix-ie^-x2)a(e^ix+ie^-x2)

Dont really know what the * mean in the y^* usually i would do it what i did but that was for problems like f=e^(-5+x) or somthing

 

[mighty2000]

Hello there, it seems like you are struggling with understanding the math in this physics problem. Don't worry, it can be daunting at first but with some practice and guidance, you will be able to understand it better. Let's break down the problem and try to understand it together.

First, let's clarify what the * symbol means. In this context, it represents multiplication. So, when we have f*f, it means we are multiplying the function f with itself.

Next, let's look at the equation ∫f*f = 1. This is called the normalization condition, which means that the integral of the squared function should equal to 1. This is important in physics because it helps us find the probability of a particle being in a certain state.

Now, for your attempt at a solution, f2=a(eix+ie-x2)*a(eix+ie-x2), you are correct in multiplying the function with itself. However, the correct expression would be f2=a^2(eix+ie-x2)^2. This is because when we multiply two terms with the same base, we need to multiply their exponents as well.

Lastly, for the given solution of a*(e-ix-ie-x2)a(eix+ie-x2), it is using a property of complex numbers where (a+bi)(a-bi) = a^2+b^2. This is why we have a*(e-ix-ie-x2)a(eix+ie-x2) instead of a^2(eix+ie-x2)^2.

I hope this helps clarify some of your confusion. Keep practicing and don't hesitate to ask for help when needed. Mathematics is an important tool in understanding physics, so it's important to take the time to understand it. Best of luck!