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arXiv · 2010.06945

Quantum Mechanics in Wavelet Basis

Pavan Chawhan·Raghunath Ratabole
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Abstract

We describe a multi-scale resolution approach to analyzing problems in Quantum Mechanics using Daubechies wavelet basis. The expansion of the wavefunction of the quantum system in this basis allows a natural interpretation of each basis function as a quantum fluctuation of a specific resolution at a particular location. The Hamiltonian matrix constructed in this basis describes couplings between different length scales and thus allows for intuitive volume and resolution truncation. In quantum mechanical problems with a natural length scale, one can get approximate solution of the problem through simple matrix diagonalization. We illustrate this approach using the example of the standard quantum mechanical simple harmonic oscillator.

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Pavan Chawhan, Raghunath Ratabole. 2020-10-14. Quantum Mechanics in Wavelet Basis. https://arxiv.org/abs/2010.06945

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