https://www.amazon.com/gp/product/9812568484/?tag=pfamazon01-20 not free but goodSilviu said:Hello! Can someone suggest me a good reading about path integral formulation of quantum mechanics? I took 2 undergrad courses on QM, so I would like something focusing on path integral (maybe some problems too). I don't necessary want a book, even some online pdf that contains some good introduction to this would be good (I prefer something free for now if possible).
Thank you!
The path integral formulation is a mathematical technique used in quantum mechanics to describe the evolution of a physical system over time. It is based on the principle of least action, which states that the path a particle takes to go from one point to another is the one that minimizes the action. The path integral formulation allows for a probabilistic description of a system, where the probability of a particle being in a certain state is determined by summing over all possible paths it could take.
The path integral formulation is different from other formulations of quantum mechanics, such as the wave function or matrix mechanics, because it does not use operators or wave functions to describe the state of a system. Instead, it uses a path integral, which takes into account all possible paths a particle could take in a given amount of time. This makes it a more intuitive and visual approach to understanding quantum mechanics.
There are several advantages to using the path integral formulation in quantum mechanics. One advantage is that it allows for the calculation of probabilities for complex systems that would be difficult to solve using other methods. Additionally, it provides a more intuitive understanding of quantum mechanics, as it allows for visualization of the possible paths a particle could take. It also has applications in other areas of physics, such as statistical mechanics and field theory.
Like any mathematical model, the path integral formulation has its limitations. One limitation is that it can only be applied to systems with a finite number of degrees of freedom. It also requires a large amount of computational power to calculate probabilities for complex systems, making it less practical for some applications. Furthermore, it does not provide a complete description of a physical system and must be combined with other formulations to fully understand a system.
The path integral formulation has many practical applications in physics, particularly in quantum field theory and statistical mechanics. It is used to calculate the behavior of particles in complex systems, such as in nuclear reactions or the behavior of electrons in a magnetic field. It is also used in the development of new technologies, such as quantum computing, where understanding the probabilistic behavior of particles is crucial. Additionally, it has applications in other fields, such as economics and biology, where probabilistic models are used to describe complex systems.