The Quartic Oscillator: a Non-Perturbative Study by Continuous Unitary Transformations

TL;DR

This paper uses continuous unitary transformations to study the quantum quartic oscillator, providing insights into its spectrum and spectral weights, and demonstrating the method's effectiveness for simple quantum systems.

Contribution

It applies and tests the non-perturbative continuous unitary transformation technique on the quantum quartic oscillator, offering a detailed comparison of approximation schemes.

Findings

Successful calculation of the spectrum and spectral weights.

Validation of the continuous unitary transformation method for simple quantum systems.

Provides a pedagogical example for the method's application.

Abstract

The quantum quartic oscillator is investigated in order to test the many-body technique of the continuous unitary transformations. The quartic oscillator is sufficiently simple to allow a detailed study and comparison of various approximation schemes. Due to its simplicity, it can be used as pedagogical introduction in the unitary transformations. Both the spectrum and the spectral weights are discussed.