Advanced integration techniques

In summary, the conversation discusses the challenges of calculating integrals in quantum mechanics and asks for resources on techniques for solving them. One method mentioned is using integration by parts for Gaussian functions multiplied by powers of x. The conversation also mentions the well-known integral for e^-x^2 and suggests the Handbook of Mathematical Functions as a resource for more examples.
  • #1
Cosmossos
100
0
Hello,
In quantum mechanics I often come across with some very complicated integrals which I need to calculate in an analytic methods (For ex. symmetric and antisymmetric functions , Gaussians ,etc.)
Do you know where I can find a summery of those techniques?
thanks
 
Physics news on Phys.org
  • #2
Gaussian functions multiplied by powers of x are usually solved by integration by parts. Also, any self-respecting physicist knows that:

[itex]
\int^{\infty}_{-\infty} e^{-x^{2}} \, dx = \sqrt{\pi}
[/itex]

*This is as hard to derive as it appears. Even wikipedia has it at: http://en.wikipedia.org/wiki/Gaussian_integral

For more details, could you please provide some examples of said integrals?
 
Last edited:
  • #3
Abramowitz, Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables.
 

What is advanced integration techniques?

Advanced integration techniques refer to a set of mathematical methods and algorithms used to solve complex integration problems, particularly in the field of calculus. These techniques involve breaking down an integral into smaller, more manageable parts and using various rules and strategies to evaluate each part.

Why are advanced integration techniques important?

Advanced integration techniques are important because they allow us to solve integrals that cannot be evaluated using basic integration rules. These techniques are particularly useful in physics, engineering, and other fields where complex mathematical models and calculations are necessary.

What are some examples of advanced integration techniques?

Some examples of advanced integration techniques include integration by parts, trigonometric substitutions, partial fractions, and improper integrals. Each technique has its own unique approach and can be applied to different types of integrals.

How do I know when to use advanced integration techniques?

Knowing when to use advanced integration techniques requires a thorough understanding of basic integration rules and a careful analysis of the integral at hand. Generally, if an integral involves complex functions or does not fit into a specific category, advanced techniques may be needed.

Are there any tips for mastering advanced integration techniques?

Like any other mathematical concept, practice is key to mastering advanced integration techniques. It is also helpful to understand the underlying principles behind each technique and to be aware of common pitfalls and mistakes to avoid. Consulting with a teacher or tutor can also be beneficial in developing a deeper understanding of these techniques.

Similar threads

Why is the Fourier coefficent calculated like this?
    • Calculus and Beyond Homework Help
Replies
4
Views
355
Solve ##\int\frac{e^{-x}}{x^2}dx## and ##\int \frac{e^{-x}}{x}dx##
    • Calculus and Beyond Homework Help
Replies
7
Views
706
This is for an Insights article: Bivariate induction proof using Calc3
    • Calculus and Beyond Homework Help
Replies
3
Views
694
Centroid calculation using integrals
    • Calculus and Beyond Homework Help
Replies
9
Views
759
What is the key integration technique needed for this double integral?
    • Calculus and Beyond Homework Help
Replies
18
Views
1K
Total movement of bacteria assuming a random distribution
    • Calculus and Beyond Homework Help
Replies
5
Views
964
Applied Bibliography on integration and ODE/PDE solving techniques for physics
    • Science and Math Textbooks
Replies
12
Views
922
A few questions to make sure I understand Fourier series
    • Calculus and Beyond Homework Help
Replies
3
Views
286
Advanced integration techniques
    • Quantum Physics
Replies
1
Views
2K
Question about approximate numerical integration methods
    • Calculus and Beyond Homework Help
Replies
4
Views
701

Hot Threads

Recent Insights

Back
Top