Related papers: Affine Quantization on the Half Line

Affine Quantization on the Half Line

URL: http://arxiv.org/abs/2005.08696v7
Date: Mon, 15 Mar 2021 10:08:11 GMT
Title: Affine Quantization on the Half Line
Authors: Laure Gouba
Abstract summary: Dirac's canonical quantization works reasonably well in the case of conventional quantum mechanics over $mathbbRn$. Affine quantization is an alternative method, similar to the canonical quantization, that may offer a positive result in situations for which canonical quantization fails.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: The similarity between classical and quantum physics is large enough to make an investigation of quantization methods a worthwhile endeavour. As history has shown, Dirac's canonical quantization method works reasonably well in the case of conventional quantum mechanics over $\mathbb{R}^n$ but it may fail in non-trivial phase spaces and also suffer from ordering problems. Affine quantization is an alternative method, similar to the canonical quantization, that may offer a positive result in situations for which canonical quantization fails. In this paper we revisit the affine quantization method on the half line. We formulate and solve some simple models, the free particle and the harmonic oscillator.

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