By D.M. Gitman,I.V. Tyutin,B.L. Voronov
This exposition is dedicated to a constant therapy of quantization problems, based on appealing to a few nontrivial goods of useful research about the conception of linear operators in Hilbert spaces. The authors begin via contemplating quantization difficulties normally, emphasizing the nontriviality of constant operator development via featuring paradoxes to the naive remedy. It then builds the mandatory mathematical history following it by way of the idea of self-adjoint extensions. By considering several difficulties comparable to the one-dimensional Calogero challenge, the Aharonov-Bohm challenge, the matter of delta-like potentials and relativistic Coulomb problemIt then exhibits how quantization difficulties linked to right definition of observables will be handled always for relatively basic quantum-mechanical structures. in any case, comparable difficulties in quantum box idea are in brief brought. This well-organized text is most fitted for college students and publish graduates drawn to deepening their knowing of mathematical difficulties in quantum mechanics. although, scientists in mathematical and theoretical physics and mathematicians also will locate it useful.
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Additional resources for Self-adjoint Extensions in Quantum Mechanics: General Theory and Applications to Schrödinger and Dirac Equations with Singular Potentials: 62 (Progress in Mathematical Physics)
Self-adjoint Extensions in Quantum Mechanics: General Theory and Applications to Schrödinger and Dirac Equations with Singular Potentials: 62 (Progress in Mathematical Physics) by D.M. Gitman,I.V. Tyutin,B.L. Voronov