Upper and Lower Bounds of Eigenvalues: Mode-clamping Theorems*
نویسنده
چکیده
Upper and lower bounds for the eigenvalues of three types of matrices M are established. If M is written as the sum of a diagonal matrix D plus a matrix A, the real parts of the eigenvalues of M must lie between the real parts of the neighboring diagonal elements of D, no matter how large the elements of A or how closely spaced the diagonal elements of D. One of the types—that representing one state coupled to possibly all other states of either a quantum-mechanical or classical system—-arises in the approximation which gives the golden-rule result that the rate of decay of a state coupled to many other states is linear in time under certain conditions. Another of the types of matrices arises in systems having equal coupling between all states.
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