Scholarlink

<p>This study investigates pseudo-Hermitian quantum mechanics, where the Hamiltonian satisfies a modified Hermiticity condition. We extend the uncertainty relation for such systems, demonstrating its equivalence to the standard Hermitian case within a pseudo-Hermitian inner product. Analytical solutions to the time-dependent Schrödinger equation with a linearly evolving potential are derived. Furthermore, we show that the uncertainty relation for position and momentum remains real and greater than <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12648_2025_3733_Article_IEq1.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">\(\frac{1}{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </math></EquationSource> </InlineEquation>, highlighting the significance of non-Hermitian systems in quantum mechanics.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Uncertainty relation for pseudo-Hermitian quantum systems

  • 期刊论文

  • 发表日期：

    2025年8月7日

查看全文
  • Boubakeur Khantoul,
  • Bilel Hamil,
  • Amar Benchikha

摘要

This study investigates pseudo-Hermitian quantum mechanics, where the Hamiltonian satisfies a modified Hermiticity condition. We extend the uncertainty relation for such systems, demonstrating its equivalence to the standard Hermitian case within a pseudo-Hermitian inner product. Analytical solutions to the time-dependent Schrödinger equation with a linearly evolving potential are derived. Furthermore, we show that the uncertainty relation for position and momentum remains real and greater than \(\frac{1}{2}\) 1 2 , highlighting the significance of non-Hermitian systems in quantum mechanics.