The Path Inetgral and Classical Lagrange

In summary, the path integral in classical mechanics is equivalent to the saddle point approximation, where we associate a number with each possible path. In quantum mechanics, we sum over all paths instead of just one, and the classical path is the one with the highest contribution to the sum. This allows for a better understanding of the behavior of particles in quantum systems.
  • #1
Quarlep
257
4
I know that The path Integral becames classical Lagrange (Classic Mechanics) how can it be turn it.
 
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  • #3
I don't have enough math to understand it
 
  • #4
Roughly the idea is:
We associate a number with every possible path.
In classical mechanics, there is only one correct path.
In quantum mechanics, there is no single correct path, and we sum over all paths. The classical path is the path with the largest contribution to the sum.
 

What is the Path Integral?

The Path Integral is a mathematical formalism used in quantum mechanics to calculate the probability of a particle moving from one point to another over a given period of time.

What is the Classical Lagrange?

The Classical Lagrange is a mathematical framework used to describe the motion of particles in a classical (non-quantum) setting. It is based on the principle of least action, which states that the path taken by a particle between two points is the one that minimizes the action.

What is the relationship between the Path Integral and the Classical Lagrange?

The Path Integral and the Classical Lagrange are two different approaches to understanding the behavior of particles. The Path Integral is a quantum mechanical approach, while the Classical Lagrange is a classical approach. However, in certain cases, the Path Integral can be used to derive the Classical Lagrange equations.

What are some applications of the Path Integral and Classical Lagrange?

The Path Integral and Classical Lagrange have a wide range of applications, including in quantum mechanics, classical mechanics, statistical mechanics, and field theory. They are used to model and predict the behavior of particles and systems in various physical systems.

What are some common misconceptions about the Path Integral and Classical Lagrange?

Some common misconceptions about the Path Integral and Classical Lagrange include the idea that they are interchangeable or that one is superior to the other. In reality, they are two different mathematical approaches with their own strengths and limitations. Additionally, they are often used in complementary ways to gain a better understanding of physical systems.

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