Quantum Theory by Stefan Weigert
Journal of Physics A: Mathematical and General, 2006
A fundamental problem in the theory of PT-invariant quantum systems is to determine whether a giv... more A fundamental problem in the theory of PT-invariant quantum systems is to determine whether a given system `respects' this symmetry or not. If not, the system usually develops non-real eigenvalues. It is shown in this contribution how to algorithmically detect the existence of complex eigenvalues for a given PT-symmetric matrix. The procedure uses classical results from stability theory which qualitatively locate the zeros of real polynomials in the complex plane. The interest and value of the present approach lies in the fact that it avoids diagonalization of the Hamiltonian at hand.
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Physical Review A, Jun 5, 2003
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Journal of Physics A: Mathematical and General, 2001
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State reconstruction for quantum spins is reviewed. Emphasis is on non-tomographic approaches whi... more State reconstruction for quantum spins is reviewed. Emphasis is on non-tomographic approaches which are based on measurements performed with a Stern-Gerlach apparatus. Two consequences of successfully implemented state reconstruction are pointed out. First, it allows one to determine experimentally the expectation value of an arbitrary operator without a device measuring it. Second, state reconstruction suggests a reformulation of Schroedinger's equation in terms of expectation values only, without explicit reference to a wave function or a density operator.
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Quantum, 2020
Coherent and anticoherent states of spin systems up to spin j=2 are known to be optimal in order ... more Coherent and anticoherent states of spin systems up to spin j=2 are known to be optimal in order to detect rotations by a known angle but unknown rotation axis. These optimal quantum rotosensors are characterized by minimal fidelity, given by the overlap of a state before and after a rotation, averaged over all directions in space. We calculate a closed-form expression for the average fidelity in terms of anticoherent measures, valid for arbitrary values of the quantum number j. We identify optimal rotosensors (i) for arbitrary rotation angles in the case of spin quantum numbers up to j=7/2 and (ii) for small rotation angles in the case of spin quantum numbers up to j=5. The closed-form expression we derive allows us to explain the central role of anticoherence measures in the problem of optimal detection of rotation angles for arbitrary values of j.
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Physical Review Letters, 1995
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Zeitschrift f�r Physik B Condensed Matter, 1990
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Comput. Phys., 1996
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Abstract: Lueders theorem states that two observables commute if measuring one of them does not d... more Abstract: Lueders theorem states that two observables commute if measuring one of them does not disturb the measurement outcomes of the other. We study measurements which are described by continuous positive operator-valued measurements (or POVMs) associated with coherent states on a Lie group. In general, operators turn out to be invariant under the Lueders map if their P-and Q-symbols coincide. For a spin corresponding to SU (2), the identity is shown to be the only operator with this property.
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J Opt B Quantum Semicl Opt, 2003
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Journal of Optics B Quantum and Semiclassical Optics, Jun 1, 2003
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Found Phys, Nov 1, 1999
ABSTRACT Quantum mechanics of a particle in an infinite square well under the influence of a time... more ABSTRACT Quantum mechanics of a particle in an infinite square well under the influence of a time-dependent electric field is reconsidered. In some gauge, the Hamiltonian depends linearly on the momentum operator which is symmetric but not self-adjoint when defined on a finite interval. In spite of this symmetric part, the Hamiltonian operator is shown to be self-adjoint. This follows from a theorem by Kato and Rellich which guarantees the stability of a self-adjoint operator under certain symmetric perturbations. The result, which has been assumed tacitly by other authors, is important in order to establish the equivalence of different Hamiltonian operators related to each other by quantum gauge transformations. Implications for the quantization procedure of a particle in a box are pointed out.
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J Phys a Math Gen, 1998
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Journal of Physics Conference Series, Nov 1, 2010
On 29 July 2008, Professor Anthony Thomas Sudbery - known as Tony to his friends and colleagues -... more On 29 July 2008, Professor Anthony Thomas Sudbery - known as Tony to his friends and colleagues - celebrated his 65th birthday. To mark this occasion and to honour Tony's scientific achievements, a 2-day Symposion was held at the University of York on 29-30 September 2008 under the sponsorship of the Institute of Physics and the London Mathematical Society. The
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Journal of Physics A: Mathematical and Theoretical, 2019
We derive Born's rule and the density-operator formalism for quantum systems with Hilbert spaces ... more We derive Born's rule and the density-operator formalism for quantum systems with Hilbert spaces of dimension two or larger. Our extension of Gleason's theorem only relies upon the consistent assignment of probabilities to the outcomes of projective measurements and their classical mixtures. This assumption is significantly weaker than those required for existing Gleason-type theorems valid in dimension two.
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Physical Review A, 2014
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Physics Letters A, 1996
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International Journal of Modern Physics B, 2006
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Quantum Chaos — Quantum Measurement, 1992
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Quantum Theory by Stefan Weigert