Using a variational method to obtain the ground state of the quantum Hamiltonian: symbolic computation approach

Abstract

The importance of learning symbolic computation in research in theoretical sciences cannot be overemphasised. While Fortran and/or C programming laboratories have become an essential part of MSc curricula now, symbolic computing is almost never taught. We demonstrate how a freeware, SAGE, can be employed for the variational solution of simple (or complex) Hamiltonians encountered in quantum mechanics in one dimension. One can easily change the trial wavefunction and the Hamiltonian and obtain estimates of ground state energy. This should lead to a qualitative understanding of the physics of the problem. A brief extension to the first excited state for potentials with parity is discussed. Finally, we give a brief overview of the range of problems which can be introduced in a physics laboratory by using SAGE.