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Radarithm
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I need to brush up on [itex]L[/itex] and [itex]H[/itex]. Does anyone know of any sources of practice for these two? Any problem sets?
Thanks.
Thanks.
Look for the Schaum's Outline of Theoretical Mechanics.Radarithm said:I need to brush up on [itex]L[/itex] and [itex]H[/itex]. Does anyone know of any sources of practice for these two? Any problem sets?
Thanks.
Looks good. Thanks.clope023 said:Look for the Schaum's Outline of Theoretical Mechanics.
A Lagrangian is a mathematical function used in classical mechanics to describe the dynamics of a physical system. It takes into account the kinetic and potential energies of the system and allows for the calculation of the system's equations of motion.
A Hamiltonian is also a mathematical function used in classical mechanics to describe the dynamics of a physical system. However, it takes into account only the system's kinetic energy and not its potential energy. In some cases, the two functions can be related through a mathematical transformation, but they are fundamentally different.
Lagrangians and Hamiltonians are used in physics because they provide a powerful and elegant way to describe the behavior of a physical system. They allow for the calculation of a system's equations of motion, which can then be used to predict the future behavior of the system. They also provide a framework for understanding conservation laws and symmetries in a system.
The principle of least action, also known as the principle of stationary action, is a fundamental concept in classical mechanics that states that a physical system will follow a path that minimizes the action, which is the integral of the Lagrangian over time. In other words, the system will follow the path of least resistance or the path that requires the least amount of energy to travel.
In quantum mechanics, Lagrangians and Hamiltonians are used to describe the behavior of quantum systems. However, in this context, they are represented by operators rather than functions and are used to calculate the system's wavefunction and its evolution over time. This allows for the prediction of a system's behavior on a microscopic scale.