Description
Quantum mechanics is weird! If you try to run as fast as you can against a wall, chances are you will smash yourself against the wall! Do not try this at home. However for quantum mechanical particles that is not quite the case. In quantum mechanics there are certain events, called instantons, which seem to violate everything we know from the classical world. For example you could have trapped a microscopic particle in a box, and poof, through an instanton tunnelling the particle would mysteriously appear outside the box. Magic! More in details: Instantons are special, finite action solutions to the classical equations of motion of some physical system. They can be thought as pseudo-particles and are used to compute the transition probability for a quantum mechanical particle tunnelling through a potential barrier. For example a classical particle forced to move in a double-well potential will never be able to move from one minimum to the other if its energy is below a certain value, in contrast a quantum mechanical particle has a non-vanishing probability to cross through a region of potential energy higher than its own energy. Instantons are responsible for this effect. In this project we want to discuss first how to mathematically describe instantons, and secondly we want to understand the physical importance of these strange, quantum mechanical objects. Between the possible topics:
Pre- Co-requisites2H Mathematical Physics or equivalently Theoretical Physics II. (Lagrangian formulation and intro to Quantum mechanics) 3H Quantum Mechanics or equivalently Foundations of Physics 2A. ResourcesFor some background:
Reading material.
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