arXiv:2010.06945

Quantum Mechanics in Wavelet Basis

Pavan Chawhan, Raghunath Ratabole A

Published Oct 14, 2020• 0 citations

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.

DOI: 10.48550/arxiv.2010.06945

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arXiv:2010.06945

Quantum Mechanics in Wavelet Basis

Pavan Chawhan, Raghunath Ratabole A

Published Oct 14, 2020• 0 citations

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.2010.06945

Related papers

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A novel Hamiltonian formulation of

1+1

dimensional

φ^4

theory in Daubechies wavelet basis: momentum space analysis

φ^4

theory and demonstrate the emergence of the well-known nonperturbative strong-coupling phase transition in the

m^2>0

sector.

Hamiltonian formulation of the

1+1

-dimensional

φ^4

theory in a momentum-space Daubechies wavelet basis

1+1

-dimensional

φ^4

theory. This approach successfully reproduces the well-known strong-coupling phase transition in the

m^2 > 0

regime. We find that the extracted critical coupling systematically converges toward its established value as the momentum resolution is increased, demonstrating the effectiveness of the wavelet-based Hamiltonian formulation for nonperturbative field-theoretic calculations.