In the middle of nowhere

Hamiltonian, systems:

The crucial thing for describing a physical system is Hamiltonian.

From the Hamiltonian, the important information of the system can be derived directly or indirectly.

For example, the kinetic energy, the potential energy, and the equation of motion, ...etc, can be derived directly from the Hamiltonian. By solving Schrodinger equation, which is the same as solving an eigenvalue problem, the Hamiltonian is an operator, and the derivative of time is another operator, the energy states can be found. Once these and other sequentially derived physical quantities have been knew, the mechanism of the system is understood.

Therefore, to find a correct Hamiltonian for a physical system is mainly important for developing a theory to explain the mechanism and predict all the properties of the system. Experimental results are used to confirm the accuracy.

In this project, the target systems are the many-particle systems, which contain many identical interacting particles. The Hamiltonian of the system generally takes this form,

.

Where T is the kinetic energy operator, and V is the potential energy operator of interaction between the particles. Xn denotes the coordinates of the nth particle, including the spacial coordinate and any other variables of the system. The potential energy term represents the interaction between a pair of the particles, counted once only, which accounts for the factor 1/2, and the double sum excluding the value m = n.

For more details, please look up the references, or classical mechanics books, quantum mechanics books, and many-body theory books.

To be continued

( second quantization )

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