Classical Oscillators in Quantum Realm

Bhartiya, Akhil (2022) Classical Oscillators in Quantum Realm. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS dissertation of Akhil Bhartiya (17MS128)) 17MS128_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (17MB)

Abstract

The time evolution of a state of a non-relativistic quantum-mechanical system can be described by the time-dependent Schr¨odinger equation (TDSE). The TDSE is simulated numerically, and for that purpose, two well known numerical methods (Direct matrix method and the Split operator method) were used. The error analysis of both the methods is done for the case harmonic potential (because the analytical solution is known). Direct matrix method (O(10)) came out to be better than the split operator in terms of error and time complexity (when simulating time independent hamiltonian). Then the Direct matrix method (O(10)) is used to simulate other systems (with time independent hamiltonian). Two particles system in one-dimension, in quadratic and quartic potentials, without and with interaction (coulomb interaction) are simulated using direct matrix method. The future aim is to work towards quantum chaos.

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