Solve ∫xp e-x2 eix dx | Get Hints for Integration

In summary, the conversation is about someone seeking help with evaluating a specific integral in quantum mechanics. They receive pointers on how to approach the problem, including using the properties of even and odd exponents and integrating by parts. It is also suggested to start from a slightly different integral for ease of calculation.
  • #1
Ananthan9470
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I need to evaluate ∫xp e-x2 eix dx from -∞ to ∞ Can someone please give me some pointers on how to do this? I am completely lost. I just need some hints or something.
 
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  • #2
Ananthan9470 said:
I need to evaluate ∫xp e-x2 eix dx from -∞ to ∞ Can someone please give me some pointers on how to do this? I am completely lost. I just need some hints or something.

Is this homework?
 
  • #3
PeroK said:
Is this homework?
No. I'm trying to learn quantum mechanics and this thing keeps popping up.
 
  • #4
You'll get a better response if you post it in homework. Even if you're learning on your own, it still counts.

Can you integrate it without the complex exponential?
 
  • #5
To get you started, if p is even you need only cosx. If p is odd you need only isinx, where [itex]e^{ix}=cosx+isinx[/itex].
Next integrate by parts to reduce exponent from p to p-1, and continue until you get p = 0.
At the end you should have [itex]\int_{-\infty}^{\infty}e^{-\frac{x^2}{2}}cosxdx[/itex].

As an afterthought, it might be easier to start from
[itex]\int_{-\infty}^{\infty}e^{-\frac{x^2}{2}}cosxdx[/itex]. Then integrate by parts to increase the exponent of x.
 
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FAQ: Solve ∫xp e-x2 eix dx | Get Hints for Integration

1. What is the purpose of the integral in this equation?

The integral is used to find the area under the curve of the function f(x) = xp e-x2 eix from the limits of integration. It is a common tool in calculus for solving problems involving rates of change and accumulation.

2. How do you solve this integral?

To solve this integral, you can use integration by parts or substitution methods. These techniques involve breaking down the integrand into simpler parts and applying rules of integration to solve for the final answer. It is a complex integral and may require advanced mathematical knowledge.

3. What is the significance of the absolute value signs around the integral?

The absolute value signs indicate that the integral is a definite integral, meaning it has specific limits of integration. This is important because it changes the way the integral is evaluated and can affect the final result.

4. Can this integral be solved analytically?

Yes, this integral can be solved analytically by using mathematical techniques such as integration by parts or substitution. However, the process may be complex and may require advanced mathematical knowledge.

5. What are some real-world applications of this type of integral?

This type of integral can be used in various fields such as physics, engineering, and economics. In physics, it can be used to calculate the work done by a force, while in engineering it can be used to determine the displacement of an object. In economics, it can be used to calculate the area under a demand curve to determine the total revenue.

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