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Classical mechanics system is a system that is changed when a force is applied to it. That system can completely be described by a set of variable called dynamical variable. Evolution of this system in configuration – momentum space can be known by finding the Hamiltonian equations of motion by L...
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/26411 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Classical mechanics system is a system that is changed when a force is applied to it. That system can completely be described by a set of variable called dynamical variable. Evolution of this system in configuration – momentum space can be known by finding the Hamiltonian equations of motion by Legendre transformation or by Dirac method when facing the singular system. Then the next discussion is inspired by the fact that a particle’s trajectory in three dimensional space and influenced by certain potential is curved as a comet moves in elliptical trajectory because of the gravitational force from the main star. The free particle moving in a curved space also moves according to the curvature of that space. So, it can be found the relation of potential energy and the metric of the space and classical mechanics can be described in pure geometric form. Then using quantization procedure, the Schrodinger equation – as quantum counter part – of this pure geometric form can be found. At the last part, we will do Dirac procedure to Hamiltonize the Einstein – Hilbert action by decomposing the space – time metric first by ADM method. It will be found that these ADM variables is the canonical variables used to quantize the sysem. |
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