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Full-Text Articles in Social and Behavioral Sciences
A Problem Of Berry And Knotted Zeros In The Eigenfunctions Of The Harmonic Oscillator, Alberto Enciso, David James Hartley, Daniel Peralta-Salas
A Problem Of Berry And Knotted Zeros In The Eigenfunctions Of The Harmonic Oscillator, Alberto Enciso, David James Hartley, Daniel Peralta-Salas
Senior Deputy Vice-Chancellor and Deputy Vice-Chancellor (Education) - Papers
European Mathematical Society 2018 We prove that, given any finite link L in R 3 , there is a high-energy complex-valued eigenfunction of the harmonic oscillator such that its nodal set contains a union of connected components diffeomorphic to L. This solves a problem of Berry on the existence of knotted zeros in bound states of a quantum system.
Dislocations Of Arbitrary Topology In Coulomb Eigenfunctions, Alberto Enciso, David James Hartley, Daniel Peralta-Salas
Dislocations Of Arbitrary Topology In Coulomb Eigenfunctions, Alberto Enciso, David James Hartley, Daniel Peralta-Salas
Senior Deputy Vice-Chancellor and Deputy Vice-Chancellor (Education) - Papers
For any finite link L in R3 we prove the existence of a complex-valued eigenfunction of the Coulomb Hamiltonian such that its nodal set contains a union of connected components diffeomorphic to L. This problem goes back to Berry, who constructed such eigenfunctions in the case where L is the trefoil knot or the Hopf link and asked the question about the general result.