| Abstract: | A method is developed making use of variational principles and Rayleigh's quotient which yields lower bounds to eigenvalues. The method is the counterpart of the Rayleigh-Ritz method in the sense that the results obtained from both methods will improve, i.e. approach to the exact value, as more and more terms are considered, both rely on variational principles, they are similar systematically and conceptually, and this method yields lower bounds to eigenvalues which cannot be obtained from the Rayleigh-Ritz method. Therefore, with the results from both methods the eigenvalues can be bracketed into a small region. The most important advantage of the method is the lower bounds to all eigenvalues can be obtained from the solution of one transcendental equation. |
