Generalized Uncertainty Relation in the Non-commutative Quantum Mechanics |
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Authors: | Email author" target="_blank">Won?Sang?ChungEmail author |
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Institution: | 1.Department of Physics and Research Institute of Natural Science, College of Natural Science,Gyeongsang National University,Jinju,Korea |
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Abstract: | In this paper the non-commutative quantum mechanics (NCQM) with the generalized uncertainty relations \({\Delta } x_{1} {\Delta } x_{2} \ge \frac {\theta }{2}, {\Delta } p_{1} {\Delta } p_{2} \ge \frac {\bar {\theta }}{2}, {\Delta } x_{i} {\Delta } p_{i} \ge \frac {\hbar _{eff}}{2}\) is discussed. Four each uncertainty relation, wave functions saturating each uncertainty relation are explicitly constructed. The unitary operators relating the non-commutative position and momentum operators to the commutative position and momentum operators are also investigated. We also discuss the uncertainty relation related to the harmonic oscillator. |
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