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In mathematics and physics, the diamagneti … In mathematics and physics, the diamagnetic inequality relates the Sobolev norm of the absolute value of a section of a line bundle to its covariant derivative. The diamagnetic inequality has an important physical interpretation, that a charged particle in a magnetic field has more energy in its ground state than it would in a vacuum. To precisely state the inequality, let denote the usual Hilbert space of square-integrable functions, and the Sobolev space of square-integrable functions with square-integrable derivatives.Let be measurable functions on and suppose that is real-valued, is complex-valued, and .Then for almost every , In particular, . .Then for almost every , In particular, .
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In mathematics and physics, the diamagneti … In mathematics and physics, the diamagnetic inequality relates the Sobolev norm of the absolute value of a section of a line bundle to its covariant derivative. The diamagnetic inequality has an important physical interpretation, that a charged particle in a magnetic field has more energy in its ground state than it would in a vacuum. In particular, .han it would in a vacuum. In particular, .
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Diamagnetic inequality
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