Abstract
Eigenvalue problems Au = λu with a self-adjoint operator A are ubiquitous in mathematical analysis and mathematical physics. A particularly rich field of application is formed by linear differential expressions which can be realized operator-theoretically by self-adjoint operators. Often such eigenvalue problems arise from wave- or Schrödinger-type equations after separation of the time variable, i.e. by a standing-wave ansatz. Possibly the most important physical application is quantum physics, but also other fields like electro-dynamics (including optics) or statistical mechanics are governed by partial differential operators and related eigenvalue problems.
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Nakao, M.T., Plum, M., Watanabe, Y. (2019). Eigenvalue Bounds for Self-Adjoint Eigenvalue Problems. In: Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations. Springer Series in Computational Mathematics, vol 53. Springer, Singapore. https://doi.org/10.1007/978-981-13-7669-6_10
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DOI: https://doi.org/10.1007/978-981-13-7669-6_10
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