A pole contributes only if it is inside the closed contour. (I could be misunderstanding your question.)BREAD said:
A contour integral, also known as a path integral, is a mathematical tool used in quantum mechanics to solve problems involving the propagation of quantum particles. It involves summing over all possible paths that a particle can take between two points in space.
The problem of quantum mechanics involves describing the behavior of particles at the quantum level, where classical mechanics breaks down. Contour integrals are used to solve this problem by allowing us to calculate the probability of a particle being in a certain position or having a certain momentum.
Contour integrals are essential in understanding and interpreting the principles of quantum mechanics. They allow us to calculate and predict the behavior of quantum particles, which is crucial in fields such as atomic and molecular physics, quantum computing, and particle physics.
Contour integrals are a powerful tool, but they are not the only method of solving problems in quantum mechanics. They are most commonly used in problems involving the time evolution of quantum systems, but other methods such as matrix mechanics and wave mechanics may be more appropriate for certain problems.
While contour integrals are a useful tool, they have their limitations. They can be challenging to calculate for complex systems, and their application can be limited to specific types of problems. Additionally, some physicists have raised philosophical concerns about the interpretational implications of using contour integrals in quantum mechanics.
