For Schrödinger operators, the inclusion of a magnetic field raises the energy. This is the consequence of a basic inequality due to Kato. A variation on this question—namely, monotonicity of the ground state energy as a function of the parameter B—is of central importance in the theory of superconductivity and is discussed in Section 2.3 here and repeatedly in the book.
KeywordsGround State Energy Multivalued Function Harnack Inequality Magnetic Potential Basic Inequality
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