# Coupled Quantum Harmonic Oscillators

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This Demonstration models a coupled system of quantum harmonic oscillators with two electron masses in SI units; two particles have displacements and from their equilibrium points. The outer springs have an angular frequency and the inner spring an angular frequency , which can be varied. Thus, the potential energy term of the Hamiltonian is .

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Contributed by: Humberto Munoz Bauza (September 2013)

After work by: Rachael M. McDermott and Ian H. Redmount

(*Mathematica* Summer Camp 2013)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The plots are

• 3D wavefunction plots with their real and complex parts

• wavefunction real and complex density plots

• 3D PDF plots

• cross sectional plots of the PDF plot at its expectation value (with the cross section planes orthogonal to the and axes)

• PDFs of the and displacements

• density plots of the and displacements over time

Reference

[1] R. M. McDermott and I. H. Redmount, "Coupled Classical and Quantum Oscillators." arxiv.org/abs/quant-ph/0403184v2.

## Permanent Citation