Quantum Mechanics Integral Trouble

In summary, Quantum Mechanics Integral Trouble refers to the difficulties that arise when trying to integrate quantum mechanical equations. This is due to the unique nature of quantum mechanics, which involves probabilistic outcomes and non-commutative operations. Solutions to these integration problems often involve the use of special techniques such as perturbation theory and Feynman path integrals. Overall, understanding and solving these integration challenges is crucial in the study of quantum mechanics and its applications in various fields.
  • #1
jakePHYS
2
0
1. Problem: int[(x^2)*(sin^2 (n*Pi*x/a)] from 0 to a

3. Physics teacher tells me to just look it up. I've wrestled with every table of integrals I can find (web, library, my books), but I'm still hung up.
 
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  • #2
Write it as x^2*sin(k*x) where k is n*pi/a. First use the trig identity sin^2(kx)=(1-cos(2kx))/2. Then to integrate something like x^2*cos(2kx) you just have to integrate by parts twice. It's not the easiest integral in the world, but it's not the hardest either.
 
  • #3
Thnx

:biggrin: This has been vexing me for 3 1/2 weeks now! THANK YOU! :biggrin:
 
  • #4

Related to Quantum Mechanics Integral Trouble

1. What is "Quantum Mechanics Integral Trouble"?

"Quantum Mechanics Integral Trouble" refers to a common challenge faced by scientists when trying to apply quantum mechanics principles to calculate the behavior of particles in a system. It arises when trying to integrate the equations of motion for particles, as the equations involve complex numbers and can result in divergent or infinite solutions.

2. Why is quantum mechanics integration difficult?

Quantum mechanics integration is difficult because it involves complex numbers, which are numbers that contain both a real and imaginary component. These complex numbers can be challenging to manipulate and can lead to divergent solutions, making it difficult to accurately predict the behavior of particles in a system.

3. How do scientists deal with quantum mechanics integral trouble?

Scientists have developed various mathematical techniques, such as regularization and renormalization, to deal with quantum mechanics integral trouble. These techniques involve modifying the equations of motion to avoid divergent solutions and make the calculations more manageable.

4. What are the implications of quantum mechanics integral trouble?

The implications of quantum mechanics integral trouble are significant as it affects our understanding and ability to accurately predict the behavior of particles at the quantum level. Scientists must carefully consider and address this issue to ensure the accuracy of their calculations and theories.

5. Is there a solution to quantum mechanics integral trouble?

While there is no definitive solution to quantum mechanics integral trouble, scientists continue to work on developing new mathematical techniques and approaches to overcome this challenge. Additionally, advancements in technology and computing power allow for more complex and accurate calculations, which can help mitigate the effects of quantum mechanics integral trouble.

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